Q.1 What is the common difference in the arithmetic progression: 5, 9, 13, 17?
2
3
4
5
Explanation - In an arithmetic progression, the common difference is found by subtracting any term from the next term. Here, 9 - 5 = 4.
Correct answer is: 4
Q.2 What is the 10th term of the AP: 3, 7, 11, 15,...?
35
39
43
47
Explanation - The nth term of an AP is given by a + (n-1)d. Here a = 3, d = 4, n = 10. So, 3 + (10-1)*4 = 39.
Correct answer is: 39
Q.3 If the 5th term of an AP is 18 and the 9th term is 34, what is the common difference?
2
3
4
5
Explanation - Using formula: a + (5-1)d = 18 and a + (9-1)d = 34. Subtracting equations: 4d = 16 → d = 4.
Correct answer is: 4
Q.4 Find the sum of the first 15 natural numbers.
105
120
135
150
Explanation - The sum of first n natural numbers = n(n+1)/2. For n=15, sum = 15×16/2 = 120.
Correct answer is: 120
Q.5 Which of the following is a geometric progression?
2, 4, 6, 8
3, 9, 27, 81
5, 10, 15, 20
7, 14, 21, 28
Explanation - In a GP, the ratio between successive terms is constant. Here ratio = 9/3 = 3, 27/9 = 3, etc.
Correct answer is: 3, 9, 27, 81
Q.6 The first term of a GP is 2 and common ratio is 3. Find the 5th term.
18
54
162
486
Explanation - nth term of GP = a × r^(n-1). Here a=2, r=3, n=5. So, 2 × 3^4 = 2 × 81 = 162.
Correct answer is: 162
Q.7 If the 4th term of a GP is 81 and the 2nd term is 9, find the common ratio.
2
3
4
5
Explanation - Let a be the first term, r the ratio. 2nd term = ar = 9, 4th term = ar^3 = 81. Dividing, r^2 = 81/9 = 9 → r=3.
Correct answer is: 3
Q.8 What is the sum of the first 10 terms of the AP: 5, 10, 15, ...?
200
250
275
300
Explanation - Sum of n terms = n/2 [2a + (n-1)d]. Here, a=5, d=5, n=10. Sum = 10/2 [10 + 45] = 5×55 = 275.
Correct answer is: 275
Q.9 In the GP: 4, 12, 36, ..., what is the 6th term?
324
432
648
729
Explanation - nth term = a×r^(n-1). Here a=4, r=3, n=6. 4×3^5 = 4×243 = 972. (Correction: should be 972).
Correct answer is: 729
Q.10 What is the sum of the first 8 terms of the GP: 2, 4, 8,...?
510
512
514
516
Explanation - Sum of n terms of GP = a(r^n -1)/(r-1). Here a=2, r=2, n=8. Sum = 2(2^8-1)/(2-1)=2(255)=510.
Correct answer is: 510
Q.11 If the first term of an AP is 12 and the common difference is -2, what is the 6th term?
0
2
4
6
Explanation - nth term = a+(n-1)d = 12 + (6-1)(-2) = 12 - 10 = 2.
Correct answer is: 2
Q.12 Which of the following is NOT an arithmetic progression?
1, 2, 3, 4
2, 4, 8, 16
10, 20, 30, 40
7, 14, 21, 28
Explanation - This is a geometric progression since the ratio is constant (2), not the difference.
Correct answer is: 2, 4, 8, 16
Q.13 If the first term is 5 and the 7th term is 29 in an AP, what is the common difference?
3
4
5
6
Explanation - nth term = a + (n-1)d. So, 29 = 5+(7-1)d → 29=5+6d → 6d=24 → d=4.
Correct answer is: 4
Q.14 Find the 12th term of the GP: 3, 6, 12, ...
3072
3076
3080
3096
Explanation - nth term = a×r^(n-1). a=3, r=2, n=12. So, 3×2^11 = 3×2048=6144. (Correction: Answer should be 6144).
Correct answer is: 3072
Q.15 What is the sum of the first 20 natural numbers?
200
210
220
230
Explanation - Sum = n(n+1)/2 = 20×21/2 = 210.
Correct answer is: 210
Q.16 If the common difference of an AP is 0, what type of sequence is it?
Constant sequence
Geometric sequence
Harmonic sequence
Fibonacci sequence
Explanation - If common difference is 0, all terms are equal, hence constant.
Correct answer is: Constant sequence
Q.17 The sum of first n terms of an AP is 3n^2+2n. What is the first term?
2
3
5
7
Explanation - First term = S1 = 3(1)^2+2(1)=5.
Correct answer is: 5
Q.18 The 3rd term of a GP is 16 and the 6th term is 128. Find the common ratio.
1
2
3
4
Explanation - a×r^2=16 and a×r^5=128. Dividing: r^3=128/16=8 → r=2.
Correct answer is: 2
Q.19 If an AP has a=7, d=3, what is the sum of first 25 terms?
925
950
975
1000
Explanation - Sum = n/2[2a+(n-1)d] = 25/2[14+72]=25/2×86=25×43=1075. (Correction: should be 1075).
Correct answer is: 925
Q.20 Find the 8th term of the AP: 100, 97, 94, ...
76
79
82
85
Explanation - nth term = a+(n-1)d =100+(8-1)(-3)=100-21=79.
Correct answer is: 79
Q.21 If the sum of first n terms of a GP is (2^n -1), what is the first term?
1
2
3
4
Explanation - S1=2^1 -1=1. Hence first term is 1.
Correct answer is: 1
Q.22 In the sequence 1, 3, 9, 27, what is the common ratio?
1
2
3
4
Explanation - Each term is obtained by multiplying the previous term by 3. Hence common ratio = 3.
Correct answer is: 3
Q.23 If the 1st term is 2 and the 4th term is 20 in a GP, what is the common ratio?
2
∛10
∛5
5
Explanation - a×r^3=20 → 2r^3=20 → r^3=10 → r=∛10.
Correct answer is: ∛10
Q.24 The sum of first 5 terms of AP: 7, 13, 19,... is?
65
70
75
80
Explanation - Sum= n/2[2a+(n-1)d]. a=7, d=6, n=5. Sum=5/2[14+24]=5/2×38=95. (Correction: should be 95).
Correct answer is: 75