Number Series Questions and Answers

Answer: A

Correct answer: 13

The terms are the prime numbers in order - 2, 3, 5, 7, 11 - each divisible only by itself and 1. The next prime after 11 is 13; 12, 14 and 15 all have smaller factors.

Answer: B

Correct answer: 196

Each term is a perfect square of consecutive whole numbers: \[ 11^2 = 121,\quad 12^2 = 144,\quad 13^2 = 169 \] so the next is \( 14^2 = \mathbf{196} \).

Answer: C

Correct answer: 125

Each term is a perfect cube of consecutive whole numbers: \[ 1^3 = 1,\quad 2^3 = 8,\quad 3^3 = 27,\quad 4^3 = 64 \] so the next is \( 5^3 = \mathbf{125} \).

Answer: D

Correct answer: -2

Each term is 3 less than the one before: \( 10 - 3 = 7 \), \( 7 - 3 = 4 \), \( 4 - 3 = 1 \). Continuing past zero gives \[ 1 - 3 = \mathbf{-2} \]

Answer: A

Correct answer: 33

Every gap is the same: the differences run 7, 7, 7, so the common difference is 7. Applying it once more to the final term, 26 + 7 gives 33. As a check, subtracting 7 from the answer returns 26, the term before it, and repeating that recovers the whole series. A constant difference is the first thing to test on any number series, because it is the commonest rule and takes only two subtractions to rule in or out.

Answer: B

Correct answer: 48

Every gap is the same: the differences run 9, 9, 9, so the common difference is 9. Applying it once more to the final term, 39 + 9 gives 48. As a check, subtracting 9 from the answer returns 39, the term before it, and repeating that recovers the whole series. Where the difference is constant the series is an arithmetic progression, and its nth term can be written down directly rather than reached step by step.

Answer: C

Correct answer: 51

Every gap is the same: the differences run 11, 11, 11, so the common difference is 11. Applying it once more to the final term, 40 + 11 gives 51. As a check, subtracting 11 from the answer returns 40, the term before it, and repeating that recovers the whole series. Subtracting each term from the next is worth doing before anything else; a row of identical results settles the matter immediately.

Answer: D

Correct answer: 66

The differences themselves form a pattern: \[ 100 - 96 = 4,\quad 96 - 89 = 7,\quad 89 - 79 = 10 \] each gap being 3 more than the last. The next gap is therefore 13, giving \[ 79 - 13 = \mathbf{66} \]

Answer: A

Correct answer: 8

This is the Fibonacci sequence: each term is the sum of the two before it. \[ 0+1 = 1,\quad 1+1 = 2,\quad 1+2 = 3,\quad 2+3 = 5 \] so the next is \( 3 + 5 = \mathbf{8} \).

Answer: B

Correct answer: 66

Every gap is the same: the differences run -6, -6, -6, so the common difference is -6. Applying it once more to the final term, 72 - 6 gives 66. As a check, subtracting -6 from the answer returns 72, the term before it, and repeating that recovers the whole series. A falling series is handled exactly as a rising one, with a negative difference, and the arithmetic is safer if the sign is written down explicitly.