Number Series Questions and Answers

Answer: A

Correct answer: 3888

The terms are multiplied rather than added to. Dividing each by its predecessor gives the same result throughout: 18 over 3 is 6, and 108 over 18 is 6, so the ratio is 6. Multiplying the last term, 648 times 6 is 3888. As a check, dividing the answer by 6 returns 648, which is the last term shown. Series that grow slowly are usually additive and those that grow quickly usually multiplicative, which narrows the search at once.

Answer: B

Correct answer: 1280

The terms are multiplied rather than added to. Dividing each by its predecessor gives the same result throughout: 20 over 5 is 4, and 80 over 20 is 4, so the ratio is 4. Multiplying the last term, 320 times 4 is 1280. As a check, dividing the answer by 4 returns 320, which is the last term shown. The first difference to compute is between the last two terms, since it constrains the answer most directly.

Answer: C

Correct answer: 648

The terms are multiplied rather than added to. Dividing each by its predecessor gives the same result throughout: 24 over 8 is 3, and 72 over 24 is 3, so the ratio is 3. Multiplying the last term, 216 times 3 is 648. As a check, dividing the answer by 3 returns 216, which is the last term shown. A rule expressed in the position number can always be checked by substituting the position of a term already shown.

Answer: D

Correct answer: 352

The terms are multiplied rather than added to. Dividing each by its predecessor gives the same result throughout: 22 over 11 is 2, and 44 over 22 is 2, so the ratio is 2. Multiplying the last term, 176 times 2 is 352. As a check, dividing the answer by 2 returns 176, which is the last term shown. Where the terms are small, listing a few extra terms of a candidate rule is quicker than reasoning about it.

Answer: A

Correct answer: 13122

The terms are multiplied rather than added to. Dividing each by its predecessor gives the same result throughout: 18 over 2 is 9, and 162 over 18 is 9, so the ratio is 9. Multiplying the last term, 1458 times 9 is 13122. As a check, dividing the answer by 9 returns 1458, which is the last term shown. The answer to a series question should always be substituted back before it is chosen.

Answer: B

Correct answer: 567

The terms are multiplied rather than added to. Dividing each by its predecessor gives the same result throughout: 21 over 7 is 3, and 63 over 21 is 3, so the ratio is 3. Multiplying the last term, 189 times 3 is 567. As a check, dividing the answer by 3 returns 189, which is the last term shown. Patterns in the hundreds are no harder than patterns in single figures once the differences are written down.

Answer: C

Correct answer: 38

The gaps are 3, 5, 7, 9, which follow no constant pattern, so the rule lies in the terms rather than in the steps between them. Each term is the square of its position plus two: position 1 gives 3 and position 5 gives 27. The next position is 6, which gives 38. As a check, the same rule applied to the earlier positions reproduces 3, 6, 11, 18, 27 exactly, so it accounts for every term shown and not merely the last. A series is fully determined by its rule and its first term, so both must be identified before extending it.

Answer: D

Correct answer: 43

The gaps are 4, 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 square of its position, plus the position, plus one: position 1 gives 3 and position 5 gives 31. The next position is 6, which gives 43. As a check, the same rule applied to the earlier positions reproduces 3, 7, 13, 21, 31 exactly, so it accounts for every term shown and not merely the last. Recognising the family is most of the work; the arithmetic that follows is usually trivial.

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.