CBSE Questions for Class 10 Maths Arithmetic Progressions Quiz 14 - MCQExams.com

The common difference of an Arithmatic Progression, whose $$3^{rd}$$ term is $$5$$ and $$7^{th}$$ term is $$9$$, is ...............
  • $$1$$
  • $$2$$
  • $$3$$
  • $$4$$
The sum of first $$10$$ terms and $$20$$ terms of an AP are $$120$$ and $$440$$ respectively. What is the common difference?
  • $$1$$
  • $$2$$
  • $$3$$
  • $$4$$
In a given A.P.,  $${ T }_{ 25 }-{ T }_{ 20 }=15$$. $$\therefore$$ $$d=$$............. for the A.P.
  • $$5$$
  • $$3$$
  • $$25$$
  • $$120$$
................ can be one of the term in Arithmetic progression 4, 7, 10, ...............
  • 103
  • 123
  • 171
  • 99
If $$1 + 6 + 11 + 16 + ... + x = 148$$, then the value of $$x$$ is
  • $$36$$
  • $$35$$
  • $$-36$$
  • None of these
Find the sum of first 25 terms of an A.P. whose $$n^{th}$$ term is given by $$T_n = (7 - 3n)$$
  • 800
  • -803
  • 735
  • None of these
The $$54^{th}$$ and $$4^{th}$$ terms of an A.P. are $$-61$$ and $$64$$ respectively. Find the $$23^{rd}$$ term.
  • $$\dfrac {35}2$$
  • $$\dfrac {33}2$$
  • $$\dfrac {37}2$$
  • $$\dfrac {39}2$$
The sum of all numbers of the form $$2k + 1$$, where $$k$$ takes on integral values from $$1$$ to $$n$$ is:
  • $$n^2$$
  • $$n(n + 1)$$
  • $$n(n + 2)$$
  • $$(n + 1)^2$$
  • $$(n + 1)(n + 2)$$
The tenth term of an A.P. : $$\sqrt {2}, 3\sqrt {2}, 5\sqrt {2}, 7\sqrt {2}$$, ..... is:
  • $$10\sqrt {2}$$
  • $$12$$
  • $$19\sqrt {2}$$
  • $$11\sqrt {2}$$
$$0$$ (zero) is a term of the A.P $$40,37,34,31,....$$. True or false?
  • True
  • False
Match the APs given in column A with suitable common differences given in column B.

         Column A                                                Column B

A. $$-2, 2, 6, 10,...$$                                                1.  $$\dfrac{2}{3}$$

B. $$a = 18, n = 10, a_n = 0$$                                   $$-5$$

C. $$a = 0, a_{10} = 6$$                                                 3.  $$4$$

D. $$a_2 = 13, a_4 =3$$                                               $$-4$$

                                                                               $$-2$$

                                                                               $$\dfrac{1}{2}$$

                                                                               7.  $$5$$
  • A-3, B-5, C-1, D-2
  • A-4, B-1, C-3, D-2
  • A-2, B-7, C- 5, D-6
  • A-7, B-4, C-2, D- 2
Find the sum of the first $$15$$ terms of the sequences having $$n$$th term as
$${ x }_{ n }=6-n$$
  • $$30$$
  • $$-30$$
  • $$20$$
  • $$-20$$
The sum of an A.P. whose first term is a, second term is b and the last term is c is equal to $$\dfrac{(a+c)(b+c-2a)}{2(b-a)}$$.
  • True
  • False

Identify which of the following list of numbers is an arithmetic progression?
  • $$1,1,2,3,5,...$$
  • $$2,3,5,7,11,...$$
  • $$10,100,1000,...$$
  • $$12,18,24,30,...$$
If $$7th$$ and $$13th$$ terms of an $$A.P$$. Be $$34$$ and $$64$$, respectively, then its $$18th$$ terms is:
  • $$87$$
  • $$88$$
  • $$89$$
  • $$90$$
If two terms of an arithmetic progression are known, then the two terms can be represented using which of the formula below?
  • $$t_{n1} = a - (n_1-1)d\ $$ and $$\ t_{n2} = a - (n_2-1)d$$.
  • $$t_{n1} = 2a + (n_1-1)d$$ and $$t_{n1} = 2a + (n_2-1)d$$.
  • $$t_{n1} = a + (n_1-1)d$$ and $$t_{n1} = a + (n_2-1)d$$.
  • $$t_{n1} = a + (n_1-2)d$$ and $$t_{n1} = a + (n_2-2)d$$.
The third term of  an arithmetic progression is $$18$$, and the seventh term is $$30$$, then the sum of $$17$$ terms is 
  • $$612$$
  • $$600$$
  • $$656$$
  • None of these
Sum of the first $$20$$ odd natural numbers is
  • $$400$$
  • $$40$$
  • $$200$$
  • $$0$$
The sum of first $$p$$ terms of an arithmetic progression is $$q$$, and the sum of first $$q$$ term is $$p$$, then the sum of first $$p + q$$ terms is
  • $$(p + q)$$
  • $$-(p + q)$$
  • $$(q - p)$$
  • $$(p - q)$$
If fourth therm of an $$A.P$$ is thrice its first term and seventh term is one less than the twice of third term, then its common difference is ?
  • $$1$$
  • $$2$$
  • $$-2$$
  • $$3$$
The first term of an $$A.P.$$ is $$10$$ and its $$41^{st}$$ term is $$81$$. Find the sum of the series, if $$81$$ is the last term.
  • $$1025$$
  • $$1865.5$$
  • $$858$$
  • $$962$$
Sum of the first $$n$$ terms of an A.P. having first term $$a$$ and last term $$\ell$$ is ____
  • $$\dfrac{n}{2} (2a - \ell)$$
  • $$\dfrac{n}{2} (2a + \ell)$$
  • $$\dfrac{n}{2} (a + \ell)$$
  • $$\dfrac{n}{2} (a - \ell)$$
Sum of first $$n$$ natural numbers is $$S_{1}$$, sum of first $$n$$ odd natural numbers is $$S_{2}$$, and sum of first $$n$$ even numbers is $$S_{3}$$. Then $$S_{1}:S_{2}:S_{3}$$=
  • $$n-1\ :\ n\ :\ n+1$$
  • $$n\ :\ 2n-1-1\ :\ 2n$$
  • $$n+1\ :\ 2n\ :\ 2(n+1)$$
  • $$n+1\ :\ n\ :\ 2n-1\ :\ 2n$$
If the first, second and last term of an $$A.P.$$ are $$a,\ b$$ and $$2a$$ respectively. then its sum is
  • $$\dfrac { ab }{ 2\left( b-a \right) } $$
  • $$\dfrac { ab }{ \left( b-a \right) } $$
  • $$\dfrac { 3ab }{ 2\left( b-a \right) } $$
  • $$none\ of\ these$$
If the ratio of $${n^{th}}$$ terms of two A.P.'s is $$\left( {2n + 8} \right):\left( {5n - 3} \right)$$, then the ratio of the sums of their $$n$$ terms is 
  • $$\,\,\left( {2n + 18} \right):\left( {5n + 3} \right)$$
  • $$\,\left( {5n - 1} \right):\left( {2n + 18} \right)$$
  • $$\,\,\left( {2n + 18} \right):\left( {5n - 1} \right)$$
  • $$\,\left( {3n + 18} \right):\left( {4n + 1} \right)$$
The formula to find $$n^{th}$$ term of an A.P is,
  • $$a + (n - 1)d$$
  • $$ar^{n - 1}$$
  • $$\dfrac{1}{a + (n - 1)d}$$
  • $$a - (n + 1)d$$
A man saved Rs. $$200$$ in each of the first three months of his service. In each of the subsequent months his saving increases by Rs. $$40$$ more than the saving of immediately previous month. His total saving from the start of service will be Rs. $$11040$$ after.
  • $$18$$ months
  • $$19$$ months
  • $$20$$ months
  • $$21$$ months
For the A.P. if $$a = 7$$ and $$d = 2.5 ,$$ then $$t _ { 12 } = ?$$
  • 37.5
  • 34.5
  • 28.2
  • 44.5
Three  numbers are in $$AP$$ such that their sum is $$18$$ and sum of their squares is $$158$$. The greatest number among them is
  • $$10$$
  • $$11$$
  • $$12$$
  • $$none\ of\ these$$
The first term of an AP is unity and common difference is $$5 .$$ Which of the following will be a term of this AP.
  • $$4880$$
  • $$7881$$
  • $$5890$$
  • $$7891$$
0:0:1


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