Sequence and Series - Multiple Choice Questions
Instructions: This quiz contains 55 multiple-choice questions on sequence and series. Click the "Show Answers" button to highlight the correct answers in yellow.
| 01 | What is the nth term of arithmetic progression? (A) a + (n-1)d (B) arn-1 (C) a + nd (D) arn |
| 02 | The sum of first n natural numbers is: (A) n(n-1)/2 (B) n(n+1)/2 (C) n² (D) 2n |
| 03 | In a GP, if a = 2 and r = 3, what is the 5th term? (A) 54 (B) 108 (C) 162 (D) 486 |
| 04 | The sum of infinite GP 1 + 1/2 + 1/4 + 1/8 + ... is: (A) 1 (B) 1.5 (C) 2 (D) ∞ |
| 05 | If 2, x, 18 are in GP, then x = ? (A) 6 (B) 6 (C) 9 (D) 12 |
| 06 | The arithmetic mean between 4 and 16 is: (A) 8 (B) 10 (C) 12 (D) 14 |
| 07 | Sum of first n terms of AP is given by: (A) n/2[2a + (n-1)d] (B) n/2[2a + (n-1)d] (C) n/2[a + l] (D) Both B and C |
| 08 | If a, b, c are in AP, then: (A) a + c = b (B) 2b = a + c (C) b² = ac (D) 2a = b + c |
| 09 | The sequence 1, 4, 9, 16, 25,... is: (A) AP (B) Sequence of squares (C) GP (D) Harmonic progression |
| 10 | Sum of the series 1 + 3 + 5 + ... + 99 is: (A) 2500 (B) 2500 (C) 2550 (D) 2600 |
| 11 | If a, b, c are in GP, then: (A) a + c = 2b (B) b² = ac (C) 2b = a + c (D) b = √(a+c) |
| 12 | The geometric mean between 4 and 9 is: (A) 6 (B) 6 (C) 6.5 (D) 7 |
| 13 | Sum of infinite GP exists only when: (A) r > 1 (B) r < -1 (C) |r| < 1 (D) r = 1 |
| 14 | The 10th term of AP: 3, 7, 11, 15,... is: (A) 35 (B) 39 (C) 43 (D) 47 |
| 15 | If sum of n terms of AP is n², then its common difference is: (A) 1 (B) 2 (C) 3 (D) 4 |
| 16 | The sequence 2, 6, 18, 54,... is: (A) AP with d=4 (B) GP with r=3 (C) AP with d=3 (D) GP with r=2 |
| 17 | Sum of first 100 even natural numbers is: (A) 5050 (B) 10100 (C) 10000 (D) 10200 |
| 18 | If 5th term of AP is 17 and 9th term is 33, then common difference is: (A) 3 (B) 4 (C) 5 (D) 6 |
| 19 | The sum of series 1² + 2² + 3² + ... + n² is: (A) n(n+1)/2 (B) n(n+1)(2n+1)/6 (C) [n(n+1)/2]² (D) n(n+1)(n+2)/6 |
| 20 | If a, b, c are in HP, then: (A) 2/b = 1/a + 1/c (B) b = 2ac/(a+c) (C) a, b, c are in AP (D) Both A and B |
| 21 | The sum of series 1 + 2 + 3 + ... + n is 55, then n = ? (A) 9 (B) 10 (C) 11 (D) 12 |
| 22 | Which term of AP 7, 12, 17,... is 87? (A) 15th (B) 17th (C) 19th (D) 21st |
| 23 | The sum of cubes of first n natural numbers is: (A) n(n+1)(2n+1)/6 (B) [n(n+1)/2]² (C) n²(n+1)²/4 (D) n(n+1)(n+2)/6 |
| 24 | If sum of n terms of AP is 3n² + 5n, then its common difference is: (A) 3 (B) 6 (C) 5 (D) 8 |
| 25 | The sequence 1/2, 1/4, 1/8, 1/16,... is: (A) AP (B) GP with r=1/2 (C) HP (D) GP with r=2 |
| 26 | Sum of the series 5 + 10 + 15 + ... + 100 is: (A) 1000 (B) 1050 (C) 1100 (D) 1150 |
| 27 | If 4, x, 9 are in GP, then x = ? (A) 6 (B) 6 (C) 13/2 (D) 36 |
| 28 | The arithmetic mean of first n natural numbers is: (A) n/2 (B) (n+1)/2 (C) n(n+1)/2 (D) n |
| 29 | Which term of GP 2, 6, 18,... is 4374? (A) 6th (B) 8th (C) 10th (D) 12th |
| 30 | Sum of first n odd natural numbers is: (A) n (B) n² (C) 2n (D) n(n+1) |
| 31 | If a, b, c are in AP, then (a-c)² = ? (A) 4(b² - ac) (B) 4(b² - ac) (C) 2(b² - ac) (D) b² - 4ac |
| 32 | The sum of series 1×2 + 2×3 + 3×4 + ... + n(n+1) is: (A) n(n+1)(n+2)/2 (B) n(n+1)(n+2)/3 (C) n(n+1)(2n+1)/6 (D) [n(n+1)/2]² |
| 33 | If 5, 8, 11,... is an AP, then its 15th term is: (A) 42 (B) 47 (C) 52 (D) 57 |
| 34 | The sum of infinite series 9 + 3 + 1 + 1/3 + ... is: (A) 12 (B) 13.5 (C) 15 (D) 18 |
| 35 | If sum of n terms of AP is 2n² + 3n, then first term is: (A) 2 (B) 5 (C) 7 (D) 9 |
| 36 | The harmonic mean between 2 and 8 is: (A) 4 (B) 3.2 (C) 5 (D) 6 |
| 37 | Sum of the series 1³ + 2³ + 3³ + ... + 10³ is: (A) 2500 (B) 3025 (C) 3600 (D) 4225 |
| 38 | If a, b, c are in GP, then log a, log b, log c are in: (A) AP (B) AP (C) HP (D) GP |
| 39 | The sum of series 1 + (1+2) + (1+2+3) + ... to n terms is: (A) n(n+1)(n+2)/6 (B) n(n+1)(n+2)/6 (C) n(n+1)(2n+1)/6 (D) [n(n+1)/2]² |
| 40 | If 3rd term of GP is 4 and 6th term is 32, then common ratio is: (A) 2 (B) 2 (C) 3 (D) 4 |
| 41 | Sum of first 20 terms of AP: 1, 4, 7, 10,... is: (A) 590 (B) 590 (C) 600 (D) 610 |
| 42 | The geometric mean of 4 and 16 is: (A) 8 (B) 8 (C) 10 (D) 12 |
| 43 | If a, b, c are in AP, then 1/bc, 1/ca, 1/ab are in: (A) AP (B) HP (C) GP (D) None |
| 44 | Sum of the series 1² + 3² + 5² + ... + (2n-1)² is: (A) n(2n-1)(2n+1)/3 (B) n(2n-1)(2n+1)/3 (C) n(n+1)(2n+1)/6 (D) [n(n+1)/2]² |
| 45 | The 8th term of GP 1/2, 1/4, 1/8,... is: (A) 1/64 (B) 1/256 (C) 1/512 (D) 1/1024 |
| 46 | If sum of n terms of AP is n(3n+1), then 25th term is: (A) 148 (B) 148 (C) 150 (D) 152 |
| 47 | The sequence 1, 3, 6, 10, 15,... represents: (A) Square numbers (B) Triangular numbers (C) Cubic numbers (D) Prime numbers |
| 48 | Sum of the series 1×3 + 3×5 + 5×7 + ... to n terms is: (A) n(4n²+6n-1)/3 (B) n(4n²+6n-1)/3 (C) n(n+1)(n+2)/3 (D) n(2n+1)(2n+3)/3 |
| 49 | If 4th term of AP is 14 and 12th term is 46, then first term is: (A) 2 (B) 2 (C) 4 (D) 6 |
| 50 | The sum of series 1/1×2 + 1/2×3 + 1/3×4 + ... + 1/n(n+1) is: (A) 1/(n+1) (B) n/(n+1) (C) (n-1)/n (D) 1/n |
| 51 | If a, b, c are in GP, then a², b², c² are in: (A) AP (B) GP (C) HP (D) None |
| 52 | Sum of first 15 multiples of 8 is: (A) 900 (B) 960 (C) 1020 (D) 1080 |
| 53 | The arithmetic mean of numbers 1, 2, 3, ..., n is 10, then n = ? (A) 18 (B) 19 (C) 20 (D) 21 |
| 54 | If sum of three numbers in AP is 15 and their product is 80, then numbers are: (A) 2, 5, 8 (B) 2, 5, 8 (C) 3, 5, 7 (D) 4, 5, 6 |
| 55 | The sum of infinite GP 0.9 + 0.09 + 0.009 + ... is: (A) 0.99 (B) 1 (C) 1.1 (D) 1.11 |
