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CBSE Questions for Class 11 Engineering Maths Sequences And Series Quiz 2 - MCQExams.com
CBSE
Class 11 Engineering Maths
Sequences And Series
Quiz 2
Find the missing letters
PTVX, AEGI, ..... WACE, HLNP
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KNQT
0%
LPRT
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KPQS
0%
HKLO
Explanation
Pattern is combination of two series
$$\displaystyle P_{11}T_{7}V_{5}X_{3},A_{26}E_{22}G_{20}I_{18},L_{15}P_{11}R_{9}T_{7},W_{4}A_{26}C_{24}E_{22},H_{19}L_{15}N_{13}P_{11}$$
$$\displaystyle \therefore $$ Missing letter = LPRT
Find the missing letters
AYD, BVF, DRH, ....., KGL
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0%
FMI
0%
GMJ
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HLK
0%
GLJ
Explanation
Pattern is
$$\displaystyle ^{1}AY_{2}^{4}D,^{2}BV_{5}^{6}F,^{4}DR_{9}^{8}H,^{7}GM_{14}^{10}J,^{11}KG_{20}^{12}L,$$.....
$$\displaystyle \therefore $$ Missing letters = GMJ
ac_cab_baca_aba_acac
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aacb
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acbc
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babb
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bcbb
Explanation
Pattern is combination of two series
acac and abab, ac
a
c/ab
a
b/aca
c
/aba
b
/acac
b_abbc_bbca_bcabb_ab
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0%
acaa
0%
acba
0%
cabc
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cacc
Explanation
Pattern is b
c
ab/bc
a
b/bca
b
/bacb/b
c
ab
adb_ac_da_cddcb_dbc_cbda
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bccba
0%
cbbaa
0%
ccbba
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bbcad
Explanation
Pattern is adb
c
/ac
b
d/a
b
cd/dcb
a
/dbc
a
/cbda
Here letters are equidistant from the begining and the end of series
a_abbb_ccccd_ddccc_bb_ba
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abcda
0%
abdbc
0%
abdcb
0%
abcad
Explanation
Pattern is a
a
a/bbb
b
/cccc/d
d
dd/ccc
c
/bb
b
b/a
abaa_aab_a_a
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abb
0%
aba
0%
bab
0%
aab
Explanation
Pattern is aba/a
b
a/ab
a
/a
b
a
aba_baca_ba_bacaabac_aca
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0%
cacb
0%
ccab
0%
cabc
0%
abcc
Explanation
Pattern is aba
c
/baca/
a
ba
c
/baca/abac/
b
aca
Thus the pattern abac,baca is repeated
Find the missing letters
B E I N T.........
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A
0%
S
0%
U
0%
V
Explanation
Sequence is the given series is moving forward with +2, +3, +4, +5, +6 and so on steps
i.e.
aa_b_abb___bb
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abaa
0%
bbaa
0%
baaa
0%
baba
Explanation
Pattern is aa/
b
b/
a
a/bb/
aa
/bb
Find the missing letters
Z W S P L I E........
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0%
D
0%
F
0%
K
0%
B
Explanation
Sequence in the given series is moving backward first-2 and then-3 steps
i.e.
abc_bc_c_
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acbbab
0%
aabbca
0%
aabacb
0%
aababc
Explanation
Pattern is abc/abc/abc/abc
Choose the correct statement(s):
$$A$$: Every sequence is a progression.
$$B$$: Every progression is a sequence.
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Only $$A$$
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Only $$B$$
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Both $$A$$ and $$B$$
0%
None
Explanation
The difference between a progression and a sequence is that a progression has a specific rule to calculate its next term from its previous term, whereas a sequence can be based on a logical rule like 'a group of prime numbers'.
Thus, every progression is a sequence but every sequence is not a sequence.
If CAT is $$48$$, Z is $$52$$ Then what is TEA equal to ?
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$$48$$
0%
$$52$$
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$$60$$
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$$50$$
Explanation
Alphanumeric coding type
Word Code value Final code
(alphabet series)
CAT C=3,A=1,T=20 24X2=48
3+1+20=24
Z 26 24X2=52
TEA T=20,E=5,A=1 26X2=52
20+5+1=26
aab....aaa......bba.....
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0%
baa
0%
abb
0%
bab
0%
bbb
Explanation
1 First blank space should be filled in by 'b' so that we have two a's followed by two b's
2 Second blank space should be filled in either by 'a' so that we have four a's followed by two b's or by 'b' so that we have three a's followed by three b's
3 Last space must be filled in by 'a'
4 Thus we have two possible answer : 'baa' and 'bba' But only 'baa' appears in the alternatives So the answer is (a).
5 In case we had both the possible answer in the alternatives we would have chosen the one that forms a more prominent pattern which is aabb/aaabbb/aa Thus our answer would have been "bba"
I thought of a decimal number. After I had multiplied it by 2, then added 1.5 and then divided by 3, I got 3.What was the decimal number?
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7.1
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5.6
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5.8
0%
4.5
Explanation
Let the decimal number be $$x.$$
$$\dfrac{x\times 2+1.5}{3}=3.5$$
$$2x+1.5=3.5\times 3$$
$$2x+1.5=10.5$$
$$2x=9$$
$$x=\dfrac{9}{2}$$
$$x=4.5$$
Hence, correct option is D.
If $$\displaystyle t_{3}=15,S_{10}=120$$ then the tenth term of the series i:
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$$\displaystyle 6\frac{3}{5}$$
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$$\displaystyle 5\frac{3}{5}$$
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$$\displaystyle 6\frac{4}{5}$$
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$$\displaystyle 6\frac{3}{4}$$
Explanation
$$\displaystyle t_{3}=a+2d=15$$ ....(i)
$$\displaystyle S_{10}=\frac{10}{2}\left [ 2a+9d \right ]=120$$
$$\displaystyle S_{10}\Rightarrow 2a+9d=24$$ ....(ii)
(i) and (ii) gives $$\displaystyle a=\frac{87}{5}$$ and $$\displaystyle d=-\frac{6}{5}$$
$$\displaystyle \therefore t_{10}=a+9d=\frac{87}{5}+9\times \left ( -\frac{6}{5} \right )$$
$$\displaystyle =6\frac{3}{5}$$
How many numbers are there between 500 and 600 in which 9 occurs only once?
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19
0%
18
0%
10
0%
9
Explanation
509 , 519 , 529 , 539 , 549 , 559 , 569 , 579 , 589 , 590 , 591 , 592 ,
593 , 594 , 595 , 596 , 597 , 598 ...as 9 has to be occurred only once
so 599 would not be there so only 18 numbers are there.
Answer the following set of questions by reading the above pitctograph.
Number of TV sets sold in the year 2005 is
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$$1000$$
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$$500$$
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$$50$$
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$$2000$$
Explanation
In the given pictogram the year 2005 depicts only one television figure.
When each television figure represents 500 TV sets, number of TV sets sold in the year 2005 is 500.
So, option B is the correct answer.
Observe the following pattern for obtaining the sums then find the sum of numbers from 781 to 790?
1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 = 55
11 + 12 + 13 + 14 + 15 + 16 + 17 + 18 + 19 + 20 = 155
21 + 22 + 23 + 24 + 25 + 26 + 27 + 28 + 29 + 30 = 255
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
51 + 52 + 53 + 54 + 55 + 56 + 57 + 58 + 59 + 60 = 555
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
101 + 102 + 103 + 104 + 105 + 106 + 107 + 108 + 109 + 110 = 1055
251 + 252 + 253 + 254 + 255 + 256 + 257
258 + 259 + 260 = 2555
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7055
0%
7855
0%
7955
0%
8155
Explanation
781 + 782 + 783 + 784 + 785
786 + 787 + 788 + 789
+ 790 = 7855
ab _ bc _ c _ ba _ c
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baac
0%
aabb
0%
caab
0%
aaab
Explanation
Pattern is ab
c
/bc
a
/c
a
b/a
b
c
Thus letters are written in a cyclic order
In a _______ each term is found by multiplying the previous term by a constant.
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0%
arithmetic sequence
0%
geometric sequence
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arithmetic series
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None of these
Explanation
In a geometric sequence each term is found by multiplying the previous term by a constant.
A sequence of numbers in which each term is related to its predecessor by same law is called
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0%
arithmetic series
0%
progression
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geometric series
0%
none of these
Explanation
A sequence of numbers in which each term is related to its predecessor by same law is called progression
Example: 1, 2, 3, 4.... is an example of sequence or progression.
Since the given sequence follows a same rule or law through out the sequence and there is a relation between each term and it's previous one.
$$10,$$ __$$, 15, 15, 20, 20, 25, 25,...$$. What number should fill the blank?
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7
0%
8
0%
10
0%
15
Explanation
Here addition with repetition series, each number in the series repeats itself, and then increases by $$5$$ to get the next number.
The next number is $$10$$.
________ can be defined as arrangement of terms in which sequence of terms follow some conditions.
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0%
Series
0%
Preceding sequence
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Progression
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Geometric progression
Explanation
Progression can be defined as arrangement of terms in which sequence of terms follow some conditions.
_______ is a series of successive events.
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Series
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Preceding sequence
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Progression
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Geometric progression
Explanation
Progression is a series of successive events.
Find the next number in the series.
$$3, 6, 9, 12, 15,....$$
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$$17$$
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$$18$$
0%
$$19$$
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$$20$$
Explanation
The next number is $$18$$.
Since the numbers are multiple of $$3$$.
$$3, 6, 9, 12, 15, \underline {18 }$$.
A _________ is a sequence of numbers where each term in the sequence is found by multiplying the previous term with a unchanging number called the common ratio.
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0%
geometric progression
0%
arithmetic series
0%
arithmetic progression
0%
None of these
Explanation
A geometric progression is a sequence of numbers where each term in the sequence is found by multiplying the previous term with a with a unchanging number called the common ratio.
Example: $$2, 6, 18, 54, 108....$$
This geometric sequence has a common ratio $$3$$.
State the following statement is true or false:
Progression means increment of quantity in a particular pattern.
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0%
True
0%
False
Explanation
Progression means increment of quantity in a particular pattern.
For example: $$2,4,6,8,....$$ and $$3,6,12,24,....$$
If there are five consecutive integer in a series and the first integer is $$1$$, what is the value of the last consecutive integer?
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$$2$$
0%
$$3$$
0%
$$4$$
0%
$$5$$
Explanation
Let the five consecutive integers be $$x, x + 1, x + 2, x + 3$$ and $$x + 4$$.
Therefore, the value of first integer is $$1$$ i.e., $$x = 1$$
So, the last integer is $$x + 4$$
The value of last integer $$= 5$$.
A progression of the form $$a, ar, ar^2$$, ..... is a
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0%
geometric series
0%
arithmetic series
0%
arithmetic progression
0%
geometric progression
Explanation
A progression of the form $$a, ar, ar^2$$, ..... is a geometric progression.
Geometric Progression refers to a sequence in which successor term of each term is obtained by multiplying a constant term.
Identify the geometric progression.
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$$1, 3, 5, 7, 9, ...$$
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$$2, 4, 6, 8, 10...$$
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$$5, 10, 15, 25, 35..$$
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$$1, 3, 9, 27, 81...$$
Explanation
A geometric sequence is a sequence of numbers such that the quotient of any two successive members of the sequence is a constant called the common ratio of the sequence.
So, $$1, 3, 9, 27, 81...$$ is a geometric progression.
Here the common ratio is $$3$$.
$$5, 25, 125, .....$$ is an example of
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0%
arithmetic progression
0%
arithmetic series
0%
geometric series
0%
geometric progression
Explanation
In geometric progression, the ratio of consecutive terms should be equal.
Here $$5, 25, 125, ...$$ is an example of geometric progression as their common ratio is $$5$$.
A ______ is the sum of the numbers in a geometric progression.
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arithmetic progression
0%
arithmetic series
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geometric series
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geometric sequence
Explanation
A geometric series is the sum of the numbers in a geometric progression.
Identify the geometric series.
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$$1 + 3 + 5 + 7 +....$$
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$$2 + 12 + 72 + 432...$$
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$$2 + 3 + 4 + 5 +...$$
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$$11 + 22 + 33 + 44+...$$
Explanation
Geometric series is of the following form:
$$a+ar+ar^2+ar^3 +ar^4+..........+ar^n$$
Series $$2+12+72+432+......$$ follows the same with
$$a=2$$ and
$$r=6$$.
Hence, option B is correct.
A sequence of numbers such that the quotient of any two successive members of the sequence is a constant called the common ratio of the sequence is known as
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0%
geometric series
0%
arithmetic progression
0%
arithmetic series
0%
geometric sequence
Explanation
A sequence of number, $${ a }_{ 1 }+{ a }_{ 2 }+......{ a }_{ n }$$ quotient of any two successive number is a constant,
$$\cfrac { { a }_{ 2 } }{ { a }_{ 1 } } =\cfrac { { a }_{ 3 } }{ { a }_{ 2 } } =........=\cfrac { { a }_{ n } }{ { a }_{ n-1 } } =$$common ratio $$(r)$$
So we can write
$${ a }_{ 1 }+{ a }_{ 1 }r+{ a }_{ 2 }r+{ a }_{ 3 }r.......{ a }_{ n-1 }r\\ ={ a }_{ 1 }+{ a }_{ 1 }r+{ a }_{ 1 }{ r }^{ 2 }..........{ a }_{ n-2 }{ r }^{ 2 }$$
and in the end in terms of $${ a }_{ 1 }$$
$$={ a }_{ 1 }+{ a }_{ 1 }r+{ a }_{ 1 }{ r }^{ 2 }+{ a }_{ 1 }{ r }^{ 3 }.........{ a }_{ 1 }{ r }^{ n-1 }$$
We can clearly say this series is in $$GP$$.
Answer $$(D)$$
$$10,20,40,80$$ is an example of
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arithmetic series
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geometric series
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arithmetic sequence
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geometric sequence
Explanation
$$10, 20, 40, 80$$ is an example of geometric sequence.
In geometric sequence, the ratio of succeeding term to the preceeding term is always equal.
Here the common ratio is $$2$$.
$$1, 3, 9, 27, 81$$ is a
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0%
geometric sequence
0%
arithmetic progression
0%
arithmetic series
0%
geometric series
Explanation
$$1, 3, 9, 27, 81$$ is a geometric sequence.
A geometric progression is a sequence of numbers such that the quotient of any two successive members of the sequence is a constant called the common ratio of the sequence.
The sequence $$6, 12, 24, 48....$$ is a
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0%
geometric series
0%
arithmetic sequence
0%
geometric progression
0%
harmonic sequence
Explanation
The sequence $$6, 12, 24, 48....$$ is a geometric progression as the ratio here is common.
The common ratio in the given series is $$2$$.
The geometric sequence is also called as
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0%
geometric progression
0%
arithmetic sequence
0%
arithmetic series
0%
geometric series
Explanation
The sequence is also called as progression.
So, the geometric sequence can be called as the geometric progression.
If a sequence of values follows a pattern of multiplying a fixed amount times each term to arrive at the following term, it is called a:
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0%
geometric sequence
0%
arithmetic sequence
0%
geometric series
0%
none of these
Explanation
$$3,3^2,3^3,3^4,....(r=3)$$
In a sequence if a fixed amount/constant is multiplied to each term to get the successive term the sequence is called geometric sequence.
Here $$3$$ is the constant which gets multiplied to each term to obtain the successive term.
Which one of the following is a general form of geometric progression?
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$$1, 1, 1, 1, 1$$
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$$1, 2, 3, 4, 5$$
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$$2, 4, 6, 8, 10$$
0%
$$-1, 2, -3, 4, -5$$
Explanation
Lets see option A:
Sequence is $$1,1,1,1,1$$
General form of GP is
$$a=1$$ and $$r=1$$
Here ratio is constant throughout.
Thus in all options, option A is correct.
The geometric progression is $$1,1,1,1,1,............$$.
The number of terms in a sequence $$6, 12, 24, ....1536$$ represents a
Report Question
0%
arithmetic progression
0%
arithmetic series
0%
geometric progression
0%
geometric series
Explanation
Given sequence is $$6,12,24,....1536$$
Since, $$\dfrac {12}{6} =2$$ and $$\dfrac {24}{12} =2$$
i.e. the given sequence is a geometric sequence / progression.
$$4, \dfrac{8}{3}, \dfrac{16}{9}, \dfrac{32}{27}..$$ is a
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0%
arithmetic sequence
0%
geometric sequence
0%
geometric series
0%
harmonic sequence
Explanation
lets check the ratio between the consecutive terms.
$$\dfrac {\frac {8}{3}}{4}=\dfrac {8}{12}=\dfrac {2}{3}$$
Again take the ratio between next consecutive terms.
$$\dfrac {\frac {16}{9}}{\frac {8}{3}}=\dfrac {16\times 3}{9\times 8}=\dfrac {2}{3}$$
Here t
he common ratio is same $$\dfrac{2}{3}$$ throughout.
Hence, $$4, \dfrac{8}{3}, \dfrac{16}{9}, \dfrac{32}{27}..$$ is a geometric sequence.
An example of G.P. is
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$$-1, \dfrac{1}{2}, \dfrac{1}{4}, \dfrac{1}{8}...$$
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$$ -1, \dfrac{3}{2}, \dfrac{1}{2}, -\dfrac{1}{2}$$
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$$1, \dfrac{1}{2}, \dfrac{1}{4}, \dfrac{1}{6}...$$
0%
$$1, \dfrac{1}{2}, \dfrac{1}{4}, \dfrac{1}{8}...$$
Explanation
For a G.P., the ratio of consecutive terms must be equal.
Here only D satisfies this condition.
So, an example of G.P. is $$1, \dfrac{1}{2}, \dfrac{1}{4}, \dfrac{1}{8}...$$
Here the common ratio is $$\dfrac{1}{2}$$.
Identify a geometric progression.
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$$1, 3, 5, 7, 9.....$$
0%
$$2, 4, 6, 8, 10.....$$
0%
$$4, 8, 16, 32, 64....$$
0%
$$1, -1, 3, -2, 4$$
Explanation
For a G.P., the ratio must be common throughout.
Thus the sequence $$4, 8, 16, 32, 64.... $$ is a geometric progression because the common ratio is $$2.$$
The common ratio is used in _____ progression.
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0%
arithmetic
0%
geometric
0%
harmonic
0%
series
Explanation
The common ratio is used in geometric progression.
For example: $$2,4,8,16,....$$
Here the common ratio is $$2$$.
Which of the following is not in the form of G.P.?
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$$2, 6, 18, 54, ....$$
0%
$$3, 12, 48, 192, ....$$
0%
$$1, 4, 7, 10, ....$$
0%
$$1, 3, 9, 27, ....$$
Explanation
In option A, the common ratio is $$3$$.
In option B, the common ratio is $$4$$.
In option D, the common ratio is $$3$$.
$$1, 4, 7, 10, ....$$. is not a G.P., since the sequence is in the form of A.P.
Which one of the following is not a geometric progression?
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0%
$$1, 2, 4, 8, 16, 32$$
0%
$$4, -4, 4, -4, 4$$
0%
$$12, 24, 36, 48$$
0%
$$6, 12, 24, 48$$
Explanation
For geometric progression, the ratio of the consecutive terms should be equal.
Here $$12, 24, 36, 48$$ is not a geometric progression. Here only the difference is common i.e. $$12$$.
Rest all options have same common ratio i.e., in option A, the ratio is $$2$$. In option B, the ratio is $$-1$$.
And in option D, the ratio is $$2$$.
Here the given sequence is an arithmetic progression.
Which one of the following is a geometric progression?
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0%
$$3, 5, 9, 11, 15$$
0%
$$4, -4, 4, -4, 4$$
0%
$$12, 24, 36, 48$$
0%
$$6, 12, 24, 36$$
Explanation
$$4, -4, 4, -4, 4$$ is a geometric progression.
Here the common ratio is $$-1$$.
Option B is correct.
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