Number Series Questions and Answers

Answer: A

Correct answer: 130

The gaps are 8, 20, 38, which follow no constant pattern, so the rule lies in the terms rather than in the steps between them. Each term is the cube of its position plus the position: position 1 gives 2 and position 4 gives 68. The next position is 5, which gives 130. As a check, the same rule applied to the earlier positions reproduces 2, 10, 30, 68 exactly, so it accounts for every term shown and not merely the last. A cube series is best recognised by trying small whole numbers rather than by analysing the gaps.

Answer: B

Correct answer: 215

The gaps are 19, 37, 61, which follow no constant pattern, so the rule lies in the terms rather than in the steps between them. Each term is one less than the cube of its position: position 2 gives 7 and position 5 gives 124. The next position is 6, which gives 215. As a check, the same rule applied to the earlier positions reproduces 7, 26, 63, 124 exactly, so it accounts for every term shown and not merely the last. Adding the position number to a cube leaves the growth dominated by the cube, so the family is identified from the largest terms.

Answer: C

Correct answer: 72

The gaps are 6, 10, 14, 18, which follow no constant pattern, so the rule lies in the terms rather than in the steps between them. Each term is twice the square of its position: position 1 gives 2 and position 5 gives 50. The next position is 6, which gives 72. As a check, the same rule applied to the earlier positions reproduces 2, 8, 18, 32, 50 exactly, so it accounts for every term shown and not merely the last. Where the gaps alternate, the series advances by their sum every two terms, which is a quick way to jump ahead.

Answer: D

Correct answer: 75

The gaps are 9, 15, 21, which follow no constant pattern, so the rule lies in the terms rather than in the steps between them. Each term is three times the square of its position: position 1 gives 3 and position 4 gives 48. The next position is 5, which gives 75. As a check, the same rule applied to the earlier positions reproduces 3, 12, 27, 48 exactly, so it accounts for every term shown and not merely the last. The presence of a very large final term often signals a multiplicative rule rather than an additive one.

Answer: A

Correct answer: 42

The gaps are 6, 8, 10, which follow no constant pattern, so the rule lies in the terms rather than in the steps between them. Each term is the product of two consecutive whole numbers: position 1 gives 6 and position 4 gives 30. The next position is 5, which gives 42. As a check, the same rule applied to the earlier positions reproduces 6, 12, 20, 30 exactly, so it accounts for every term shown and not merely the last. Products of consecutive integers grow at roughly the same rate as squares, and the two families are easily confused.

Answer: B

Correct answer: 3125

The gaps are 20, 100, 500, which follow no constant pattern, so the rule lies in the terms rather than in the steps between them. Each term is five raised to the power of its position: position 1 gives 5 and position 4 gives 625. The next position is 5, which gives 3125. As a check, the same rule applied to the earlier positions reproduces 5, 25, 125, 625 exactly, so it accounts for every term shown and not merely the last. Powers of four rise so steeply that only three or four terms fit comfortably in a question.

Answer: C

Correct answer: 128

The gaps are 2, 4, 8, 16, 32, which follow no constant pattern, so the rule lies in the terms rather than in the steps between them. Each term is two raised to the power of its position: position 1 gives 2 and position 6 gives 64. The next position is 7, which gives 128. As a check, the same rule applied to the earlier positions reproduces 2, 4, 8, 16, 32, 64 exactly, so it accounts for every term shown and not merely the last. Factorials grow faster than any power, which is usually the clue that the multiplier is itself increasing.

Answer: D

Correct answer: 70

The gaps are 3, 5, 9, 17, which follow no constant pattern, so the rule lies in the terms rather than in the steps between them. Each term is a power of two plus the position itself: position 1 gives 3 and position 5 gives 37. The next position is 6, which gives 70. As a check, the same rule applied to the earlier positions reproduces 3, 6, 11, 20, 37 exactly, so it accounts for every term shown and not merely the last. Series built on position number formulas can be extended to any position without computing the intervening terms.

Answer: A

Correct answer: 55

The gaps are 11, 11, 11, which follow no constant pattern, so the rule lies in the terms rather than in the steps between them. Each term is eleven times its position: position 1 gives 11 and position 4 gives 44. The next position is 5, which gives 55. As a check, the same rule applied to the earlier positions reproduces 11, 22, 33, 44 exactly, so it accounts for every term shown and not merely the last. A linear rule in the position number produces a constant difference, so the two descriptions are the same thing seen differently.

Answer: B

Correct answer: 150

The gaps are 10, 24, 44, which follow no constant pattern, so the rule lies in the terms rather than in the steps between them. Each term is the cube of its position plus its square: position 1 gives 2 and position 4 gives 80. The next position is 5, which gives 150. As a check, the same rule applied to the earlier positions reproduces 2, 12, 36, 80 exactly, so it accounts for every term shown and not merely the last. An arithmetic slip is far more common than a misread rule, so the final calculation deserves a second look.