CBSE Class 10 Mathematics Arithmetic Progression MCQs Set K

Question. The famous mathematician associated with finding the sum of the first 100 natural numbers is
(a) Pythagoras
(b) Newton
(c) Gauss
(d) Euclid
Answer: C

Question. If the common difference of an A.P. is 5, then what is \( a_{18} - a_{13} \)?
(a) 5
(b) 20
(c) 25
(d) 30
Answer: C

Question. What is the common difference of four terms in an A.P. such that the ratio of the product of the first and fourth terms to that of the second and third is 2 : 3 and the sum of all four terms is 20?
(a) 3
(b) 1
(c) 4
(d) 2
Answer: D

Question. If the seventh term of an A.P. is 1/9 and its ninth term is 1/7, find common difference.
(a) 1
(b) 2/63
(c) 3/64
(d) 1/63
Answer: D

Question. The sum \( (– 6) + (0) + (6) + \dots \) upto \( 13^{\text{th}} \) term =
(a) 390
(b) 1380
(c) 378
(d) 1830
Answer: A

Question. If \( a, (a – 2) \) and \( 3a \) are in A.P., then the value of \( a \) is
(a) – 3
(b) – 2
(c) 3
(d) 2
Answer: B

Question. If \( m^{\text{th}} \) term of an A.P. is \( 1/n \) and \( n^{\text{th}} \) term is \( 1/m \), then the sum of first \( mn \) terms is
(a) \( mn + 1 \)
(b) \( \frac{mn + 1}{2} \)
(c) \( \frac{mn - 1}{2} \)
(d) \( \frac{mn - 1}{3} \)
Answer: B

Question. If 9 times the \( 9^{\text{th}} \) term in an arithmetic progression is equal to 15 times of its \( 15^{\text{th}} \) term, then what is the \( 24^{\text{th}} \) term?
(a) 0
(b) 9
(c) 15
(d) 23
Answer: A

Question. If \( x \neq y \) and the sequences \( x, a_1, a_2, y \) and \( x, b_1, b_2, y \) each are in A.P., then \( \left( \frac{a_2 - a_1}{b_2 - b_1} \right) \) is
(a) 2/3
(b) 3/2
(c) 1
(d) 3/4
Answer: C

Question. If the sum of 7 terms of an A.P. is 49 and that of 17 terms is 289, then, its first term is
(a) 1
(b) – 1
(c) 2
(d) –2
Answer: A

Question. Find how many terms are there in the A.P. 16, 24, 32, ......, 96.
(a) 10
(b) 11
(c) 12
(d) 14
Answer: B

Question. If the first, second and last terms of an A.P. are \( a, b \) and \( 2a \) respectively, its sum is
(a) \( \frac{ab}{2(b - a)} \)
(b) \( \frac{ab}{b - a} \)
(c) \( \frac{3ab}{2(b - a)} \)
(d) None of the optons 
Answer: C

Question. Find the sum of first 15 multiples of 8.
(a) 840
(b) 1020
(c) 960
(d) 920
Answer: C

Question. Find the sum of first 10 terms of the A.P. \( x – 8, x – 2, x + 4, \dots \)
(a) 10x + 210
(b) 10x + 190
(c) 5x + 190
(d) 5x + 210
Answer: B

Question. In an A.P., the sum of first \( n \) terms is \( \frac{3n^2}{2} + \frac{13n}{2} \). Find its \( 15^{\text{th}} \) term.
(a) 45
(b) 50
(c) 60
(d) 75
Answer: B

Question. Three numbers in an A.P. have sum 18. Its middle term is
(a) 6
(b) 8
(c) 3
(d) 2
Answer: A

Question. Find the sixteenth term of the A.P. –10, –6, –2, 2,...
(a) 10
(b) 20
(c) 40
(d) 50
Answer: D

Question. \( \frac{3}{\sqrt{5}} + \sqrt{5} + \frac{7}{\sqrt{5}} + \dots \) to 15 terms is equal to
(a) \( 51\sqrt{5} \)
(b) \( 17\sqrt{5} \)
(c) \( 81\sqrt{5} \)
(d) \( 9\sqrt{5} \)
Answer: A

Question. Which of the following is not an A.P. ?
(a) \( -3, - \frac{5}{2}, -2, - \frac{3}{2}, \dots \)
(b) 0.3, 0.33, 0.333, ......
(c) \( \sqrt{3}, \sqrt{12}, \sqrt{27}, \sqrt{48}, \dots \)
(d) \( p, 2p + 1, 3p + 2, 4p + 3, \dots \)
Answer: B

Assertion & Reasoning Based MCQs

Directions In these questions, a statement of Assertion is followed by a statement of Reason is given.
Choose the correct answer out of the following choices :
(a) Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
(b) Assertion and Reason both are correct statements but Reason is not the correct explanation of Assertion.
(c) Assertion is correct statement but Reason is wrong statement.
(d) Assertion is wrong statement but Reason is correct statement.

Question. Assertion : The common difference of the A.P. 19, 18, 17, .... is 1.
Reason : Let \( a_1, a_2, a_3, a_4, \dots \) is an A.P. Then, common difference of this A.P. will be the difference between any two consecutive terms, i.e., \( d = a_2 – a_1 \) or \( a_3 – a_2 \) or \( a_4 – a_3 \) and so on.
(a)
(b)
(c)
(d)
Answer: D

Question. Assertion : The ninth term of an A.P. is equal to seven times the second term and twelfth term exceeds five times the third term by 2. Then the first term is 1.
Reason : If \( S_n \) and \( S_{n–1} \) are the sum of first \( n \) terms and \( (n – 1) \) terms of an A.P., then \( n^{\text{th}} \) term, \( a_n = S_n - S_{n-1} \).
(a)
(b)
(c)
(d)
Answer: C

Question. Assertion : Sum of first 20 multiples of 4 is 480.
Reason : In an A.P., sum of \( n \) terms, \( S_n = \frac{n}{2} [a + l] \), where, \( n, a \) and \( l \) are number of terms, first term and last term respectively.
(a)
(b)
(c)
(d)
Answer: D

Question. Assertion : If the first term of an A.P. is 4, last term is 81 and the sum of the given terms is 510. Then, there are 12 terms in the given A.P.
Reason : If \( a \) is the first term, \( l \) is the last term and \( n \) is the number of terms of an A.P., then \( S_n = \frac{n}{2} (a + l) \).
(a)
(b)
(c)
(d)
Answer: A