CBSE Class 10 Mathematics Arithmetic Progression MCQs Set 05

Question. If a, b, c, d, e, f are A.M.s between 2 and 12, then a + b + c + d + e + f is equal to :-
(a) 14
(b) 84
(c) 42
(d) None

Answer: C

Question. The next term of the sequence 9, 16, 27, 42, ......... is :-
(a) 53
(b) 61
(c) 57
(d) None

Answer: B

Question. The number of terms common to the arithmetic progressions 3, 7, 11, ......., 407 and 2, 9, 16,....., 709 is :-
(a) 51
(b) 14
(c) 21
(d) 28

Answer: B

Question. The nth term of the series 1+1/1+3 + 1/1+3+5 + ....... is :-
(a) 2/ n(n1) +
(b) 1/ n²
(c) n²
(d) None

Answer: B

Question. The sum of 40 A.M's between two numbers is 120. The sum of 50 A.M's between them is equal to :-
(a) 130
(b) 160
(c) 150
(d) None

Answer: C

Question. For the A.P. x + (x + 1) + (x + 2) + ...... + y
(a) C. D. is 1
(b) Numer of terms is y − x + 1
(c) Sum of the series is y−x+1/2(x+y)
(d) All of the options

Answer: D

Question. The sum of all natural numbers which are less than 100 and divisible by 6 is
(a) 412
(b) 510
(c) 672
(d) 816

Answer: D

Question. How many terms are there is an AP whose first and fifth terms are –14 and 2 respectively and the sum of terms is 40?
(a) 15
(b) 10
(c) 5
(d) 20

Answer: B

Question. The infinite sum 1+4/7+9/7²+16/7³+25/7⁴ +......... equals
(a) 27/ 14
(b) 21/ 13
(c) 49 /27
(d) 256 /147

Answer: C

Question. The sum of 12 terms of an A.P. whose first term is 4, is 256. What is the last terms ?
(a) 35
(b) 36
(c) 37
(d) 116/3

Answer: C

Question. The sum of n terms of a series is An² + Bn, then the nth term is :-
(a) A(2n − 1) − B
(b) A(1 − 2n) + B
(c) A(1 − 2n) − B
(d) A(2n − 1) + B

Answer: D

Question. If x, y, z are in A.P., then (x + y − z) (y + z − x) is equal to :-
(a) 8xy + 3y² − 4x²
(b) 8xy − 3y² − 4x²
(c) 8xy − 3x² + 4y²
(d) 8xy − 3y² + 4x²

Answer: B

Question. I open a book store with a number of books. On the first day, I sell 1 book; on the second day, I sell 2 books; on the third day, I sell 3 books and so on. At the end of the month (30 days). I realise that I sold the same number of books with which I started. Find the number of books in the beginning.
(a) 365
(b) 420
(c) 465
(d) 501

Answer: C

Question. If a, b, c are in AP then ab + bc =
(a) b
(b) b²
(c) 2b² 
(d) 1/b

Answer: C

Question. The sum of first five terms of the AP: 3, 7, 11, 15, ... is:
(a) 44
(b) 55
(c) 22
(d) 11

Answer: B

Question. How many multiples of 7 are there between 33 and 329 ?
(a) 43
(b) 35
(c) 329
(d) 77

Answer: A

Question. If aⁿ + bⁿ/aⁿ⁻¹ +bⁿ⁻¹ be the arithmetic mean between a and b, then the value of n is :-
(a) 1
(b) 0
(c) − 1/ 2
(d) −1

Answer: A

Question. If the sum of first n natural numbers is one-fifth of the sum of their squares, then n is
(a) 5
(b) 6
(c) 7
(d) 8

Answer: C

Question. If S denotes the sum of first n terms of the A.P. a + (a + d) + (a + 2d) + ....... whose nth term is l, then the common 'd' of the A.P. is :-
(a) l −a/n
(b) l²−a²/2S−a+l
(c) l²−a²/2S−a+l
(d) None of the options

Answer: A

Question. The sums of first n terms of two A.P.'s are in the ratio (3n + 8) : (7n + 15). The ratio of their 12th terms is :-
(a) 4/ 9
(b) 7 /16
(c) 3 /7
(d) None

Answer: B

Question. The sum of 3rd and 15th elements of an arithmetic pr gression is equal to the sum of 6th, 11th and 13th elements of the same progression. Then which element of the series should ecessarily be equal to zero ?
(a) 1st
(b) 9th
(c) 12th
(d) None of the options

Answer: C

Question. If 3+5+7+.........+nterms/ 5+8+11+......+10 terms = 7, then the value of n is
(a) 35
(b) 36
(c) 37
(d) 40

Answer: A

Question. If an A.P., S_m : S_n :: m² : n². The ratio of the pth term to qth term is :-
(a) p−1/q−1
(b) p/ q
(c) 2p −1/ 2q −1
(d) None

Answer: C

Question. 2,√6 , 4.5 are the following terms of an A.P..
(a) 101st, 207th, 309th
(b) 101st, 201st, 301st
(c) 2nd, 6th, 9th
(d) None of the options

Answer: D

Question. There are two arithmetic progressions, A1 and A2, whose first terms are 3 and 5 respectively and whose common differences are 6 and 8 respectively. How many terms of the series are common in the first n terms of A₁ and A₂, if the sum of the nth terms of A1 and A2 is equal to 6,000?
(a) 103
(b) 107
(c) 109
(d) 113

Answer: B

Question. Let S_n denote the sum of the first 'n' terms of an A.P. S_2n= 3S_n. Then, the ratio S_3n/S_n is equal to
(a) 4
(b) 6
(c) 8
(d) 10

Answer: B

Question. Find the sum of all natural numbers not exceeding 1000, which are divisible by 4 but not by 8.
(a) 62500
(b) 62800
(c) 64000
(d) 65600

Answer: A

Question. In the following questions, a statement of assertion (A) is followed by a statement of reason
(a) If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.
(b) If both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion.
(c) If Assertion is correct but Reason is incorrect.
(d) If Assertion is incorrect but Reason is correct.

Question. Assertion : The sum of the series with the nth term, t_n = (9 – 5n) is (465), when no. of terms n = 15.
Reason : Given series is in A.P. and sum of n terms of an A.P. is S_n = n/2[2a + (n −1) d] .
Answer: D

Question. Assertion : Sum of first 10 terms of the arithmetic progression – 0.5, – 1.0, – 1.5, ............................ is 27.5.
Reason : Sum of n terms of an A.P. is given as S_n = n/2[2a + (n −1) d] where a = first term, d = common difference.
Answer: A

Question. Assertion : If n^th term of an A.P. is 7 – 4n, then its common difference is –4.
Reason : Common difference of an A.P. is given by d = a_n + 1 – a_n.
Answer: A

Question. Assertion : If S_n is the sum of the first n terms of an A.P., then its nth term an is given by an = S_n – S_n – 1 .
Reason : The 10^th term of the A.P. 5, 8, 11, 14, ................... is 35.
Answer: C

Question. Assertion : Let the positive numbers a, b, c be in A.P., then 1/bc , 1/ac , 1/ab are also in A.P.
Reason : If each term of an A.P. is divided by abc, then the resulting sequence is also in A.P.
Answer: A

Question. Assertion : Arithmetic between 8 and 12 is 10.
Reason : Arithmetic between two numbers ‘a’ and ‘b’ is given as . a + b/2
Answer: A

Question. Assertion : Sum of first hundred even natural numbers divisible by 5 is 500.
Reason : Sum of first n-terms of an A.P. is given by S_n = n/2[2a + (n −l) d] where l = last term.
Answer: D