Arithmetic and Geometric Progression Problems

Progressions (AP, GP, HP)

Sequences and Series Problems Question Bank:

Ques. The sum of the numbers between 100 and 1000 which is divisible by 9 will be
(a) 55350
(b) 57228
(c) 97015
(d) 62140

Ans. (a)

Ques. Let  and  be roots of x2 – 3x + p = 0 and let c and d be the roots of x2 – 12x + q = 0, where a, b, c, d form an increasing G.P. Then the ratio of (q + p) : (q – p) is equal to
(a) 8 : 7
(b) 11 : 10
(c) 17 : 15
(d) None of these
Ans:- (c)

Ques. If the product of three consecutive terms of G.P. is 216 and the sum of product of pair-wise is 156, then the numbers will be
(a) 1, 3, 9
(b) 2, 6, 18
(c) 3, 9, 27
(d) 2, 4, 8

Ans. (b)

Ques. If the pth term of an A.P. be q and qth term be p, then its rth term will be
(a) p + q + r
(b) p + q – r
(c) p + r – q
(d) p – q – r

Ans. (b)

Ques. If x, y, z are in H.P., then the value of expression log (x + z) + log(x –2y + z) will be
(a) log (x – z)
(b) 2 log (x – z)
(c) 3 log (x – z)
(d) 4 log (x – z)

Ans. (b)

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Ques. If a, b, c are in G.P., a – b, c – a, b – c are in H.P., then a + 4b + c is equal to
(a) 0
(b) 1
(c) –1
(d) None of these

Ans. (a)

Ques. The sum of numbers from 250 to 1000 which are divisible by 3 is
(a) 135657
(b) 136557
(c) 161575
(d) 156375

Ans. (d)

Ques. The ratio of sum of m and n terms of an A.P. is m2 : n2 , then the ratio of mth and nth term will be
(a) m – 1 / n – 1
(b) n – 1 / m – 1
(c) 2m – 1 / 2n – 1
(d) 2n – 1 / 2m – 1

Ans. (c)

Ques. If roots of the equation a(b – c)x2 + b(c – a)x + c(a – b) = 0 are equal, then a, b, c are in
(a) A.P.
(b) G.P.
(c) H.P.
(d) None of these
Ans:- (c)

Ques. The sum of all natural numbers between 1 and 100 which are multiples of 3 is
(a) 1680
(b) 1683
(c) 1681
(d) 1682

Ans. (b)

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Ques. The number of terms of the A.P. 3,7,11,15…to be taken so that the sum is 406 is
(a) 5
(b) 10
(c) 12
(d) 14

Ans. (d)

Ques. The sum of integers from 1 to 100 that are divisible by 2 or 5  is
(a) 3000
(b) 3050
(c) 4050
(d) None of these

Ans. (b)

Ques. There are 15 terms in an arithmetic progression. Its first term is 5 and their sum is 390. The middle term is
(a) 23
(b) 26
(c) 29
(d) 32

Ans. (b)

Ques. If sum of n terms of an A.P. is 3n2 + 5n and Tm = 164 then m =
(a) 26
(b) 27
(c) 28
(d) None of these

Ans. (b)

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Ques. The nth term of the following series (1 x 3) + (3 x 5) + (5 x 7) + (3 x 5) + (5 x 7) + (7 x 9) + … will be
(a) n (2n + 1)
(b) 2n (2n – 1)
(c) (2n + 1) (2n – 1)
(d) 4n2 + 1

Ans. (c)

Ques. If sum of  terms of an A.P. is 3n2 + 5n and Tm = 164 then m =
(a) 26
(b) 27
(c) 28
(d) None of these

Ans. (b)

Ques. There are 15 terms in an arithmetic progression. Its first term is 5 and their sum is 390. The middle term is
(a) 23
(b) 26
(c) 29
(d) 32

Ans. (b)

Ques. The sum of integers from 1 to 100 that are divisible by 2 or 5  is
(a) 3000
(b) 3050
(c) 4050
(d) None of these

Ans. (b)

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Ques. If the ratio of the sum of n terms of two A.P.’s be (7n + 1) : (4n + 27), then the ratio of their 11th terms will be
(a) 2 : 3
(b) 3 : 4
(c) 4 : 3
(d) 5 : 6

Ans. (c)

Ques. If sum of n terms of an A.P. is 3n2 + 5n and Tm = 164 then m =
(a) 26
(b) 27
(c) 28
(d) None of these

Ans. (b)

Ques. Consider an infinite G.P. with first term a and common ratio r, its sum is 4 and the second term is 3/4, then
(a) a = 7/4, r = 3/7
(b) a = 3/2, r = ½
(c) a = 2, r = 3/8
(d) a = 3, r = 1/4

Ans. (d)

Ques. The sum of 3 numbers in geometric progression is 38 and their product is 1728. The middle number is
(a) 12
(b) 8
(c) 18
(d) 6

Ans. (a)

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Ques. The G.M. of roots of the equation x2 – 18x + 9 = 0 is
(a) 3
(b) 4
(c) 2
(d) 1

Ans. (a)

Ques. The product of three geometric means between 4 and 1/4 will be
(a) 4
(b) 3
(c) 2
(d) 1

Ans. (d)

Ques. The solution of the equation (x + 1) + (x + 4) + (x + 7) + … + (x + 28) = 155 is
(a) 1
(b) 2
(c) 3
(d) 4

Ans. (a)

Ques. The number of terms in the series 101 + 99 + 97 + … + 47 is
(a) 25
(b) 28
(c) 30
(d) 20

Ans. (b)

Ques. The interior angles of a polygon are in A.P. If the smallest angle be 120o and the common difference be 5o, then the number of sides is
(a) 8
(b) 10
(c) 9
(d) 6

Ans. (c)

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Ques. If A be an arithmetic mean between two numbers and S be the sum of n arithmetic means between the same numbers, then
(a) S = n A
(b) A = n S
(c) A = S
(d) None of these

Ans. (a)

Ques. The third term of a G.P. is the square of first term. If the second term is 8, then the 6th term is
(a) 120
(b) 124
(c) 128
(d) 132

Ans. (c)

Ques. If nth  terms of two A.P.’s are 3n + 8 and 7n + 15, then the ratio of their 12th terms will be
(a) 4/9
(b) 7/16
(c) 3/7
(d) 8/15

Ans. (a)

Ques. If three numbers be in G.P., then their logarithms will be in
(a) A.P.
(b) G.P.
(c) H.P.
(d) None of these

Ans. (a)

Ques. The two geometric means between the number 1 and 64 are
(a) 1 and 64
(b) 4 and 16
(c) 2 and 16
(d) 8 and 16

Ans. (b)

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Ques. The sum of all two digit numbers which, when divided by 4, yield unity as a remainder is
(a) 1190
(b) 1197
(c) 1210
(d) None of these

Ans. (c)

Ques. The sum of the first and third term of an arithmetic progression is 12 and the product of first and second term is 24, then first term is
(a) 1
(b) 8
(c) 6
(d) 4

Ans. (d)

Ques. If the 9th term of an A.P. be zero, then the ratio of its  29th  and 19th  term is
(a) 1 : 2
(b) 2 : 1
(c) 1 : 3
(d) 3 : 1

Ans. (b)

Ques. The sum can be found of a infinite G.P. whose common ratio is r
(a) For all values of r
(b) For only positive value of r
(c) Only for 0 < r < 1
(d) Only for – 1 < r < 1(r not equals to 0)

Ans. (d)

Ques. The first term of a G.P. whose second term is 2 and sum to infinity is 8, will be
(a) 6
(b) 3
(c) 4
(d) 1

Ans. (c)

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Ques. The sum of the first four terms of an A.P. is 56. The sum of the last four terms is 112. If its first term is 11, the number of terms is
(a) 10
(b) 11
(c) 12
(d) None of these

Ans. (b)

Ques. The sum of the first four terms of an A.P. is 56. The sum of the last four terms is 112. If its first term is 11, the number of terms is
(a) 10
(b) 11
(c) 12
(d) None of these

Ans. (b)

Ques. The sums of n terms of two arithmatic series are in the ratio 2n + 3 : 6n + 5, then the ratio of their 13th terms is
(a) 53 : 155
(b) 27 : 77
(c) 29 : 83
(d) 31 : 89

Ans. (a)

Ques. If sum of infinite terms of a G.P. is 3 and sum of squares of its terms is 3, then its first term and common ratio are
(a) 3/2, 1/2
(b) 1, 1/2
(c) 3/2, 2
(d) None of these

Ans. (a)

Ques. The ratio of the sums of first n even numbers and n odd numbers will be
(a) 1 : n
(b) (n + 1) : 1
(c) (n + 1) : n
(d) (n – 1) : 1

Ans. (c)

Ques. 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

Ans. (c)

Ques. 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

Ans. (b)

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Ques. The sum of infinity of a geometric progression is 4/3 and the first term is 3/4 . The common ratio is
(a) 7/16
(b) 9/16
(c) 1/9
(d) 7/9

Ans. (a)

Ques. 0.14189189189…. can be expressed as a rational number
(a) 7/3700
(b) 7/50
(c) 525/111
(d) 21/148

Ans. (d)

Ques. If a, b, c are in A.P., then (a – c)2/ (b2 – ac) =
(a) 1
(b) 2
(c) 3
(d) 4

Ans. (d)

Ques. If the first term of an A.P. be 10, last term is 50 and the sum of all the terms is 300, then the number of terms are
(a) 5
(b) 8
(c) 10
(d) 15

Ans. (c)

Ques. If Sk denotes the sum of first k terms of an arithmetic progression whose first term and common difference are a and d respectively, then Skn/Sn  be independent of n if
(a) 2a – d = 0
(b) a – d = 0
(c) a – 2d = 0
(d) None of these

Ans. (a)

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Ques. If a, b, c, d, e, f are in A.P., then the value of e – c will be
(a) 2 (c – a)
(b) 2(f – d)
(c) 2(d – c)
(d) d – c

Ans. (c)

Ques. If the sum of n terms of an A.P. is nA + n2B, where A, B are constants, then its common difference will be
(a) A – B
(b) A + B
(c) 2A
(d) 2B

Ans. (d)

Ques. Four numbers are in arithmetic progression. The sum of first and last term is 8 and the product of both middle terms is 15. The least number of the series is
(a) 4
(b) 3
(c) 2
(d) 1

Ans. (d)

Ques. If the ratio of the sum of first three terms and the sum of first six terms of a G.P.  be 125 : 152, then the common ratio r is
(a) 3/5
(b) 5/3
(c) 2/3
(d) 3/2

Ans. (a)

Ques. The sixth term of an A.P. is equal to 2, the value of the common difference of the A.P. which makes the product a1a4a5 least is given by
(a) x = 8/5
(b) x = 5/4
(c) x = 2/3
(d) None of these

Ans. (c)

Ques. If the 7th term of a H.P. is 1/10 and the 12th term is 1/25, then the 20th term is
(a) 1/37
(b) 1/41
(c) 1/45
(d) 1/49

Ans. (d)

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Ques. If the sum of the first n terms of a series be 5n2 + 2n, then its second term is
(a) 7
(b) 17
(c) 24
(d) 42

Ans. (b)

Ques. 0.5737373 =
(a) 284/497
(b) 284/495
(c) 568/990
(d) 567/990

Ans. (c)

Ques. Let Sn denotes the sum of n terms of an A.P. If S2n = 3Sn, then ratio S3n/Sn =
(a) 4
(b) 6
(c) 8
(d) 10

Ans. (b)

Ques. If the sides of a right angled triangle are in A.P., then the sides are proportional to
(a) 1: 2: 3
(b) 2: 3: 4
(c) 3: 4: 5
(d) 4: 5: 6

Ans. (c)

Ques. 7th term of an A.P. is 40, then the sum of first 13 terms is
(a) 53
(b) 520
(c) 1040
(d) 2080

Ans. (b)

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Ques. The first term of a G.P. whose second term is 2 and sum to infinity is 8, will
(a) 6
(b) 3
(c) 4
(d) 1

Ans. (c)

Ques. The sum of the integers from 1 to 100 which are not divisible by 3 or 5 is
(a) 2489
(b) 4735
(c) 2317
(d) 2632

Ans. (d)

About the author

Yash

Yash is co-founder of Examsegg. Yash loves to solve questions on reasoning and mathematics. He taught himself how to blend different techniques to get accurate solution in lesser time.

4 Comments

  • You can download complete paper with answers from the PDF link given at the end of post.

  • how can we know that the question i have solved is correct because the answer is not give here
    so tell me how to find the ans of these questions

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