Arithmetic progression and geometric progression - Question Bank

1. If the sum of the first n terms of a GP is 5(2^n - 1), what is the common ratio?
A) 1
B) 2
C) 3
D) 4
2. The sum of the first n terms of an AP is given by S_n = (3n+1)n. Find the common difference.
A) 3
B) 4
C) 6
D) 8
3. If the sum of the first n terms of a GP is 3^n - 1, then the common ratio is:
A) 1
B) 2
C) 3
D) 4
4. The first term of an AP is -15, and the sum of the first 6 terms is 15. What is the common difference?
A) 5
B) 6
C) 7
D) 8
5. If the sum of the first n terms of a GP is S_n, and the sum of the first 2n terms is S_{2n}, then the sum of the first 3n terms is:
A) S_{3n} = S_{2n} + (S_{2n} - S_n) * r
B) S_{3n} = S_{2n} + (S_{2n} - S_n) / r
C) S_{3n} = S_{2n} + (S_{2n} - S_n)^2 / S_n
D) S_{3n} = S_n + (S_{2n} - S_n)^2 / S_n
6. In an AP, the sum of the first p terms is equal to the sum of the first q terms. Then the sum of the first (p+q) terms is:
A) 0
B) 1
C) p+q
D) pq
7. The sum of the first n terms of a GP is 2(3^n - 1). What is the common ratio?
A) 2
B) 3
C) 4
D) 5
8. If a, b, c are consecutive terms of a GP, then:
A) b^2 = ac
B) a^2 = bc
C) c^2 = ab
D) a+b+c = 0
9. If the sum of n terms of an AP is S_n, and the sum of m terms is S_m, then the ratio of their m-th and n-th terms is:
A) S_n/S_m
B) S_m/S_n
C) (2n-1)/(2m-1)
D) (2m-1)/(2n-1)
10. The sum of the first 20 terms of an AP is 400 and the sum of the first 40 terms is 1600. Find the sum of the first 10 terms.
A) 100
B) 150
C) 200
D) 250
11. If a, b, c are in GP, then b is the geometric mean of a and c. The value of b is:
A) sqrt(ac)
B) ac
C) a+c
D) (a+c)/2
12. If a, b, c are in AP, then b is the arithmetic mean of a and c. The value of b is:
A) (a+c)/2
B) a+c
C) 2(a+c)
D) (a+c)/4
13. The sum of the first 6 terms of a GP is 9 times the sum of the first 3 terms. What is the common ratio?
A) 2
B) 3
C) 4
D) 5
14. The 4th term of an AP is 11 and the 7th term is 20. What is the 1st term?
A) 2
B) 3
C) 4
D) 5
15. If the first term of a GP is 1, and the sum of the first three terms is 7/4, find the common ratio.
A) 1/2
B) 2
C) 1/3
D) 3
16. The sum of the first n terms of an AP is 3n^2 - n. What is the common difference?
A) 3
B) 4
C) 5
D) 6
17. In a GP, if the first term is a and the common ratio is r, the sum of the first n terms is:
A) a(r^n - 1)/(r-1)
B) a(1 - r^n)/(r-1)
C) a(r^n - 1)/(1-r)
D) a(r^n - 1)/(r+1)
18. In an AP, if the first term is a and the common difference is d, the sum of the first n terms is:
A) n/2 * [2a + (n-1)d]
B) n/2 * [a + (n-1)d]
C) n * [2a + (n-1)d]
D) n/2 * [2a + nd]
19. The sum of the first n terms of a GP is S_n. If the common ratio is r, then the n-th term is given by:
A) S_n - S_{n-1}
B) S_n * r - S_{n-1}
C) S_n - S_{n-1} * r
D) S_n * r
20. If the sum of the first n terms of an AP is S_n, then the n-th term is given by:
A) S_n - S_{n-1}
B) S_n + S_{n-1}
C) S_{n-1} - S_n
D) S_n
21. The sum of the first 3 terms of a GP is 39/10. If the common ratio is 3/2, find the first term.
A) 1
B) 2
C) 3
D) 4
22. If x, y, z are in GP, then xz is equal to:
A) y
B) y^2
C) y^3
D) sqrt(y)
23. If x, y, z are in AP, then x+z is equal to:
A) y
B) 2y
C) 3y
D) y/2
24. The sum of the first 10 terms of an AP is 100 and the sum of the first 20 terms is 400. Find the sum of the first 30 terms.
A) 700
B) 800
C) 900
D) 1000
25. If the nth term of a GP is 3n, then the common ratio is:
A) 3
B) 9
C) 27
D) N/A
26. The sum of the first n terms of an AP is 3n^2 + 5n. Find the n-th term.
A) 6n - 2
B) 6n + 2
C) 3n + 5
D) 3n - 5
27. If the product of three terms in GP is 216, and the sum of their squares is 156, find the terms.
A) 2, 6, 18
B) 3, 6, 12
C) 4, 6, 9
D) 6, 6, 6
28. In an AP, the sum of terms equidistant from the beginning and end is:
A) Equal to the first term
B) Equal to the last term
C) Equal to the sum of the first and last term
D) Zero
29. The sum of an infinite GP is 15, and the sum of the squares of its terms is 45. Find the first term.
A) 5
B) 10
C) 15
D) 20
30. If a, b, c are in GP, then b/a is equal to:
A) c/a
B) c/b
C) a/c
D) b/c
31. If a, b, c are in AP, then b-a is equal to:
A) c-a
B) c-b
C) a-c
D) b-c
32. The sum of the first n terms of an AP is S_n. If S_{2n} = 3S_n, then find the ratio S_{3n}/S_n.
A) 4
B) 5
C) 6
D) 7
33. In a GP, if the p-th term is x and the q-th term is y, then the r-th term is:
A) x^((q-r)/(p-q)) * y^((p-r)/(p-q))
B) x^((q-r)/(q-p)) * y^((p-r)/(q-p))
C) x^((r-q)/(p-q)) * y^((p-r)/(p-q))
D) x^((q-r)/(p-q)) * y^((r-p)/(p-q))
34. The sum of the first 5 terms of a GP is 31, and the sum of the first 10 terms is 1023. What is the common ratio?
A) 2
B) 3
C) 4
D) 5
35. If the sum of n terms of an AP is an^2 + bn, then the common difference is:
A) a
B) b
C) 2a
D) 2b
36. Find the geometric mean of 4 and 9.
A) 5
B) 6
C) 7
D) 8
37. The sum of three terms in AP is 21. If the product of the first and third term is 65, find the terms.
A) 3, 7, 11
B) 5, 7, 9
C) 1, 7, 13
D) 7, 7, 7
38. In an AP, the m-th term is n and the n-th term is m. What is the (m+n)-th term?
A) 0
B) m+n
C) -(m+n)
D) m-n
39. If the first term of a GP is 1, and the sum to infinity is 2, what is the common ratio?
A) 1/2
B) 1/3
C) 2/3
D) 3/4
40. What is the sum of the first 8 terms of the GP 3, 6, 12, ...?
A) 765
B) 759
C) 771
D) 780
41. The sum of the first 10 terms of an AP is 120. If the first term is 3, find the common difference.
A) 1.5
B) 2
C) 2.5
D) 3
42. Which term of the AP 2, 5, 8, ... is 59?
A) 18th
B) 19th
C) 20th
D) 21st
43. The sum of the first n terms of a GP is given by S_n = 4(3^n - 1). What is the first term?
A) 4
B) 8
C) 12
D) 16
44. If the 2nd term of a GP is 6 and the 4th term is 54, what is the common ratio?
A) 2
B) 3
C) 4
D) 5
45. The sum of the first n terms of an AP is given by S_n = 2n^2 + 3n. What is the common difference?
A) 2
B) 3
C) 4
D) 5
46. If the 3rd term of an AP is 10 and the 7th term is 22, what is the common difference?
A) 2
B) 3
C) 4
D) 5
47. The sum of the first 4 terms of a GP is 40, and the common ratio is 3. What is the first term?
A) 1
B) 2
C) 3
D) 4
48. In a geometric progression (GP), the first term is 2 and the common ratio is 3. What is the 5th term?
A) 162
B) 81
C) 54
D) 243
49. The sum of the first 15 terms of an AP is 255, and the common difference is 2. What is the first term?
A) 1
B) 2
C) 3
D) 4
50. In an arithmetic progression (AP), the first term is 5 and the common difference is 3. What is the 10th term?
A) 32
B) 29
C) 35
D) 27
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