CBSE Class 10 Mathematics Arithmetic Progressions Worksheet Set E

Question. In an A.P. if a = 5, a_n = 81 and S_n = 860, then n is
(a) 10
(b) 15
(c) 20
(d) 25

Answer: C

Question. What is the value of k if (k + 2), (4k – 6) and (3k – 2) are three consecutive terms of an A.P.?
(a) k = –3
(b) k = 2
(c) k = –2
(d) k = 3

Answer: D

Question. The first term of an A.P. is 5 and its 100^th term is –292. The 50^th term of this A.P. will be
(a) 142
(b) –142
(c) 130
(d) –140

Answer: B

Question. If a, b, c are in A.P., then the value of (a + 2b – c) (2b + c – a) (c + a – b) will be
(a) 4abc
(b) 2abc
(c) abc
(d) None of these

Answer: A

Question. Sum of n terms of the series √2 + √8 + √18 + √32 +.... is
(a) n(n+1)/2
(b) 2n( (n + 1)
(c) (n+1)/√2
(d) 1

Answer: C

Question. If eight times the 8^th term of an A.P. is equal to 12 times the 12^th term of the A.P. then its 20^th term will be
(a) –1
(b) 1
(c) 0
(d) 2

Answer: C

Question. The 10^th term of an AP is 20 and the 19^th term is 101.
Then, the third term is
(a) – 43
(b) – 61
(c) – 52
(d) 1

Answer: A

Question. Given that the sum of the first ‘n’ terms of an arithmetic progression is 2n² + 3ⁿ, find the 12^th term.
(a) 72
(b) 36
(c) √625
(d) 56

Answer: A

Question. The common difference of the A.P. 1/p, 1-p/p, 1-2p/p ........ is
(a) 1
(b)
1/p
(c) –1
(d) − (1/p)

Answer: C

Question. The n^th term of the A.P. a, 3a, 5a, ......., is
(a) na
(b) (2n – 1)a
(c) (2n + 1)a
(d) 2na

Answer: B

Question. If the sum of the series 2 + 5 + 8 + 11 ........... is 60100, then the number of terms are
(a) 100
(b) 200
(c) 150
(d) 250

Answer: B

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

Answer: D

Question. There are 60 terms in an A.P. of which the first term is 8 and the last term is 185. The 31^st term is
(a) 56
(b) 94
(c) 85
(d) 98

Answer: D

Question. There are four arithmetic means between 2 and –18. The means are
(a) –4, –7, –10, –13
(b) 1, –4, –7, –10
(c) –2, –5, –9, –13
(d) –2, –6, –10, –14

Answer: D

Question. If the first, second and the last terms of an A.P. are a, b, c respectively, then the sum is
(a) (a + b) (a + c − 2b)/2(b − a)
(b) (b + c) (a + b − 2c)/2(b − a)
(c) (a + c) (b + c − 2a)/2(b − a)
(d) None of these

Answer: C

Question. The sum of 11 terms of an A.P. whose middle term is 30, is
(a) 320
(b) 330
(c) 340
(d) 350

Answer: B

Question. If four numbers in A.P. are such that their sum is 50 and the greatest number is 4 times the least, then the numbers are
(a) 5, 10, 15, 20
(b) 4, 10, 16, 22
(c) 3, 7, 11, 15
(d) None of these

Answer: A

Question. Let T_r be the r^th term of an A.P. for r = 1, 2, 3, .... If for some positive integers m, n we have, T_m = 1/n and T_n = 1/m, then Tmn equals
(a) 1/mn
(b) m/1 + n/1
(c) 1
(d) 0

Answer: C

Question. If the sum of the first 2n terms of 2, 5, 8, ....... is equal to the sum of the first n terms of 57, 59, 61......., then n is equal to
(a) 10
(b) 12
(c) 11
(d) 13

Answer: C

Question. The number of terms of the series 5, 7, 9, .... that must be taken in order to have the sum 1020 is
(a) 20
(b) 30
(c) 40
(d) 50

Answer: B

Question. If the n^th term of an A.P. is 4n + 1, then the common difference is :
(a) 3
(b) 4
(c) 5
(d) 6

Answer: B

Question. If a, b, c, d, e, f are in A.P., then e – c is equal to:
(a) 2(c – a)
(b) 2(d – c)
(c) 2(f – d)
(d) (d – c)

Answer: B

Question. The number of common terms of the two sequences 17, 21, 25, ....., 417 and 16, 21, 26, ........, 466 is
(a) 19
(b) 20
(c) 21
(d) 91

Answer: B

Question. The number of two digit numbers which are divisible by 3 is
(a) 33
(b) 31
(c) 30
(d) 29

Answer: C

Question. If the n^th term of an A.P. is given by an = 5n – 3, then the sum of first 10 terms is
(a) 225
(b) 245
(c) 255
(d) 270

Answer: B

Question. If S₁, S₂, S₃, ......., Sr are the sum of first n terms of r arithmetic progressions respectively. Whose first terms are 1, 2, 3, ......... and whose common differences are 1, 3, 5, ........ respectively, then the value of S₁ + S₂ + S₃ + ...... Sr is
(a) (nr-1(nr+1)/2 
(b) (nr+1)nr/2
(c) n(nr-1)/nr
(d) n(nr+1)/2 

Answer: B

Question. First term of an arithmetic progression is 2. If the sum of its first five terms is equal to one-fourth of the sum of the next five terms, then the sum of its first 30 terms is
(a) 2670
(b) 2610
(c) –2520
(d) –2550

Answer: D

Question. The odd natural numbers have been divided in groups as (1, 3) ; (5,7, 9, 11) ; (13, 15, 17, 19, 21, 23), .....
Then the sum of numbers in the 10^th group is
(a) 4000
(b) 4003
(c) 4007
(d) 4008

Answer: A

Question. Suppose the sum of the first m terms of an arithmetic progression is n and the sum of its first n terms is m, where m ≠ n. Then, the sum of the first (m + n) terms of the arithmetic progression is
(a) 1 – mn
(b) mn – 5
(c) – (m + n)
(d) m + n

Answer: C

Question. Which of the following represents an A.P. ?
(a) 0.2, 0.4, 0.6, ....
(b) 29, 58, 116....
(c) 15, 45, 135, 405...
(d) 3, 3.5, 4.5, 8.5 ....

Answer: A

Question. If t_n = 6n + 5, then t_n+1 =
(a) 6(n + 1) + 17
(b) 6(n – 1) + 11
(c) 6n + 11
(d) 6n – 11

Answer: C

Question. Sn = 54 + 51 + 48 + ........ n terms = 513. Least value of n is
(a) 18
(b) 19
(c) 15
(d) None of these

Answer: A

Question. If the nth term of an A.P. be (2n – 1), then the sum of its first n terms will be
(a) n² – 1
(b) (n – 1)²
(c) (n – 1)² – (2n – 1)
(d) n²

Answer: D

Question. If b+c−a/a , c+a−b/b , a+b−c/c are in A.P., then which of the following is in A.P.?
(a) a, b, c
(b) a², b², c²
(c) 1/a , 1/b , 1/c
(d) a³, b³, c³

Answer: B

Please click on below link to download CBSE Class 10 Mathematics Arithmetic Progressions Worksheet Set E