CBSE Questions for Class 10 Maths Arithmetic Progressions Quiz 8 - MCQExams.com

Find the sum of all natural numbers not exceeding $$1000,$$ which are divisible by $$4$$ but not by $$8.$$
  • $$62500$$
  • $$62800$$
  • $$64000$$
  • $$65600$$
$$30$$ trees are planted in a straight line at intervals of $$5\ m.$$ To water them, the gardener needs to bring water for each tree, separately from a well, which is $$10\ m$$ from the first tree in line with the trees. How far will he have to walk in order to water all the trees beginning with the first tree? Assume that he starts from the first well, and he can carry enough water to water only one tree at a time. 
  • $$4785\ m$$
  • $$4795\ m$$
  • $$4800\ m$$
  • None of these
  • Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
  • Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
  • Assertion is correct but Reason is incorrect
  • Assertion is incorrect but Reason is correct
Identify the progression:
$$A : 4, 7, 10, 13, 16, 19, 22, 25, .....$$
$$B : 4, 7, 9, 10, 13, 14, .........$$
  • Only $$A$$
  • Only $$B$$
  • Both $$A$$ and $$B$$
  • None of these
If sum of $$n$$ terms of an A.P. is $$3n^2+5n$$ and $$T_m=164 $$, what is the value of m?
  • $$26$$
  • $$27$$
  • $$28$$
  • $$25$$
Check if the series is an $$AP.$$ Find the common difference $$d$$. Also, find the next three terms.

$$-10, -6, -2 , 2.....$$. 
  • It is an $$AP$$ and $$d=4$$, other terms $$6,10,14$$
  • It is an $$AP$$ and $$d=\dfrac{3}{5}$$, other terms $$5,10,15$$
  • It is not an $$AP$$, other terms $$3,4,5$$
  • None of these
If the $$n^{th}$$ term of an A.P. be $$(2n-1),$$ then the sum of its first $$n$$ terms will be
  • $$n^2-1$$
  • $$(n-1)^2+(2n-1)$$
  • $$(n-1)^2-(2n-1)$$
  • $$n^2$$
Let $$S_n$$ denote the sum of the first $$'n'$$ terms of an A.P. $$S_{2n} = 3S_n$$. Then, the ratio $$\dfrac{S_{3n}}{S_n}$$ is equal to :
  • $$4$$
  • $$6$$
  • $$8$$
  • $$10$$
If $$\displaystyle \frac{3+5+7+......+ n(terms)}{5+8+11+.....+ 10(terms)}=7$$, then the value of $$n$$ is 
  • $$35$$
  • $$36$$
  • $$37$$
  • $$40$$
The sum up to $$9$$ terms of the series $$\displaystyle \frac{1}{2}+\frac{1}{3}+\frac{1}{6}+ ...$$ is
  • $$\displaystyle -\frac{5}{6}$$
  • $$\displaystyle -\frac{1}{2}$$
  • $$1$$
  • $$\displaystyle -\frac{3}{2}$$
If $$S=\cfrac { n }{ 2 } [2a+(n-1)d]$$ ; find $$d$$ , when $$a=8, S=380$$ and $$n=10$$.
  • $$\displaystyle 7 \frac{1}{6}$$
  • $$\displaystyle 4 \frac{5}{2}$$
  • $$\displaystyle 2\dfrac{1}{6}$$
  • $$\displaystyle 6 \dfrac{2}{3}$$
A sprinter runs 6 meters in the first second of a certain race and increase her speed by 25 cm/sec. in each succeeding second. (This means that she goes 6m 25 cm. the second second, 6m 50 cm. the third second, and so on.) How far does she go during the eight second?
  • 8.75 m
  • 7.75 m
  • 8.25 m
  • 9.25 m
The $$p^{th}$$ and $$q^{th}$$ terms an $$A.P$$ are respectively $$a$$ and $$b.$$ Then sum of $$(p+q)$$ terms is
  • $$\dfrac {p+q}{2}\left(a+b+\dfrac {a-b}{p-q}\right)$$
  • $$\dfrac {p+q}{2}\left(a-b-\dfrac {a+b}{p+q}\right)$$
  • $$ (p+q)\left(a+b+\dfrac {p-q}{a-b}\right)$$
  • $$\dfrac {p+q}{2}\left(a+b+\dfrac {p-q}{a-b}\right)$$
STATEMENT - $$1$$ : The sum of first $$11$$ terms of the A.P: $$2, 6, 10, 14,\dots$$ is $$242.$$
STATEMENT - $$2$$ : The sum of first $$n$$ terms of the A.P. is given by $$S_n = \dfrac{n}{2} [2a + (n-1)d]$$
  • Statement - $$1$$ is True, Statement - $$2$$ is True, Statement - $$2$$ is a correct explanation for Statement - $$1$$
  • Statement - $$1$$ is True, Statement - $$2$$ is True : Statement $$2$$ is NOT a correct explanation for Statement - $$1$$
  • Statement - $$1$$ is True, Statement - $$2$$ is False
  • Statement - $$1$$ is False, Statement - $$2$$ is True
There is an auditorium with $$35$$ rows of seats. There are $$20$$ seats in the first row, $$22$$ seats in the second row, $$24$$ seats in the third row, and so on. Find the number of seats in the twenty fifth row.
  • $$72$$
  • $$68$$
  • $$54$$
  • $$89$$
Which term of the A.P. 5, 12, 19, 26, ............ is 145
  • 12
  • 18
  • 25
  • 21
$$\displaystyle S =\frac{n}{2}\left [ 2a+\left ( n-1 \right )d \right ]$$; make $$d$$ the subject of formula.
  • $$\displaystyle d=\frac{\left ( 2S-a \right )}{n\left ( n-1 \right )} $$
  • $$\displaystyle d=\frac{\left ( 2S-na \right )}{n\left ( n+1 \right )} $$
  • $$\displaystyle d=\frac{2\left ( S-na \right )}{n\left ( n-1 \right )} $$
  • $$\displaystyle d=\frac{2\left ( S-a \right )}{n\left ( n+1 \right )} $$
Find the sum of first $$11$$ positive numbers which are multiples of $$6$$.
  • $$314$$
  • $$396$$
  • $$452$$
  • $$245$$
A man arranges to pay off a debt of Rs. 3600 in 40 annual instalments which form an arithmetic series. When 30 of the instalments are paid he dies leaving one-third of the debt unpaid. Find the value of the first instalment. 
  • Rs. 49
  • Rs. 51
  • Rs. 53
  • Rs. 55
Find the sum of $$A.P.$$ whose first and last term is $$13$$ and $$216$$ respectively & common difference is $$7$$.  
  • $$3434$$
  • $$3435$$
  • $$1545$$
  • $$3456$$
If $$t_{11}$$ and $$t_{16}$$ for an $$A.P.$$ are respectively $$38$$ and $$73$$, then $$t_{31}$$ is $$........$$
  • $$178$$
  • $$177$$
  • $$176$$
  • $$175$$
In the A.P. 7, 14, 21, ... How many terms are to be considered for getting sum 5740.
  • 40
  • 50
  • 14
  • 51
The $$n^{th}$$ term of the sequence   $$\displaystyle\frac{1}{p}$$, $$\displaystyle\frac{1 + 2p}{p}$$, $$\displaystyle\frac{1 + 4p}{p}$$,... is
  • $$\displaystyle\frac{1 + 2np + 2p}{p}$$
  • $$\displaystyle\frac{1 - 2np - 2p}{p}$$
  • $$\displaystyle\frac{1 + 2np - 2p}{p}$$
  • $$\displaystyle\frac{1 + 2np}{p}$$
Find the $$n^{th}$$ term of the sequence $$m -1, m - 3, m - 5,.....$$
  • $$m - n + 1$$
  • $$m + 2n + 1$$
  • $$m - 2n + 1$$
  • $$m - 2n$$
$$(p + q)^{th}$$ and $$(p - q)^{th}$$ terms of an A.P. are respectively $$m$$ and $$n.$$ The $$p^{th}$$ term is
  • $$\displaystyle\frac{1}{2}(m + n)$$
  • $$\displaystyle\sqrt{mn}$$
  • $$m + n$$
  • $$mn$$
Sum of first $$5$$ terms of an A.P. is one fourth of the sum of next five terms. If the first term is $$ 2,$$ then the common difference of the A.P. is
  • $$6$$
  • $$-6$$
  • $$3$$
  • None of these
In an A.P. S$$_3$$ $$= 6$$, S$$_6$$ $$= 3$$, then it's common difference is equal to ?
  • $$3$$
  • $$-1$$
  • $$1$$
  • None of these
The sum of all $$2$$-digit odd number is
  • $$2475$$
  • $$2530$$
  • $$4905$$
  • $$5049$$
The first term of an A.P. of consecutive integers is $$p$$$$^2$$ $$+$$The sum $$2p + 1$$ terms of this series can be expressed as
  • $$(p + 1)$$$$^2$$
  • $$(2p + 1) (p^2+p + 1)$$
  • $$(p + 1)$$$$^3$$
  • $$p$$$$^3$$$$ + (p + 1)$$$$^3$$
The sum of first 24 terms of the sequence whose n$$^{th}$$ term is given by $${a}_{n} = 3 + \displaystyle\frac{2n}{3}$$, is
  • $$278$$
  • $$272$$
  • $$270$$
  • $$268$$
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