Number Series Questions and Answers

Answer: A

Correct answer: 1250

The terms are multiplied rather than added to. Dividing each by its predecessor gives the same result throughout: 10 over 2 is 5, and 50 over 10 is 5, so the ratio is 5. Multiplying the last term, 250 times 5 is 1250. As a check, dividing the answer by 5 returns 250, which is the last term shown. Geometric series overtake arithmetic ones rapidly, which is often the visual clue that a ratio rather than a difference is at work.

Answer: B

Correct answer: 38

Each term is two more than a perfect square: \[ 1^2+2 = 3,\quad 2^2+2 = 6,\quad 3^2+2 = 11,\quad 4^2+2 = 18,\quad 5^2+2 = 27 \] so the next is \( 6^2 + 2 = \mathbf{38} \). Read as differences, the gaps are 3, 5, 7, 9 and then 11, which gives the same answer.

Answer: C

Correct answer: 224

The terms are multiplied rather than added to. Dividing each by its predecessor gives the same result throughout: 14 over 7 is 2, and 28 over 14 is 2, so the ratio is 2. Multiplying the last term, 112 times 2 is 224. As a check, dividing the answer by 2 returns 112, which is the last term shown. Multiplying the last term by the ratio is safer than extending the pattern of differences, which grows in a way that is easy to misjudge.

Answer: D

Correct answer: 5184

The terms are multiplied rather than added to. Dividing each by its predecessor gives the same result throughout: 24 over 4 is 6, and 144 over 24 is 6, so the ratio is 6. Multiplying the last term, 864 times 6 is 5184. As a check, dividing the answer by 6 returns 864, which is the last term shown. The wrong answers here follow from applying the ratio to the wrong term or from adding the previous gap instead of multiplying.

Answer: A

Correct answer: 2401

The terms are multiplied rather than added to. Dividing each by its predecessor gives the same result throughout: 7 over 1 is 7, and 49 over 7 is 7, so the ratio is 7. Multiplying the last term, 343 times 7 is 2401. As a check, dividing the answer by 7 returns 343, which is the last term shown. A ratio can be confirmed by dividing the last term by the first and taking the appropriate root, which is a useful check on a long series.

Answer: B

Correct answer: 162

Each term is 3 times the one before: \( 2 \times 3 = 6 \), \( 6 \times 3 = 18 \), \( 18 \times 3 = 54 \). So the next term is \[ 54 \times 3 = \mathbf{162} \]

Answer: C

Correct answer: 3750

The terms are multiplied rather than added to. Dividing each by its predecessor gives the same result throughout: 30 over 6 is 5, and 150 over 30 is 5, so the ratio is 5. Multiplying the last term, 750 times 5 is 3750. As a check, dividing the answer by 5 returns 750, which is the last term shown. When the terms are multiplied by a whole number the units digits often repeat in a short cycle, which gives a quick sanity check on the answer.

Answer: D

Correct answer: 64

The terms shrink by a constant factor rather than by a constant amount: 2048 over 1024 is 2, and the same holds for every neighbouring pair, so each term is the previous one divided by 2. Dividing the last term, 128 over 2 is 64. As a check, multiplying the answer by 2 returns 128, the term before it. A falling geometric series divides rather than multiplies, and reading it backwards turns it into the more familiar rising form.

Answer: A

Correct answer: 18

The terms shrink by a constant factor rather than by a constant amount: 1458 over 486 is 3, and the same holds for every neighbouring pair, so each term is the previous one divided by 3. Dividing the last term, 54 over 3 is 18. As a check, multiplying the answer by 3 returns 54, the term before it. Dividing from the small end avoids the large numbers entirely and makes the constant factor obvious.

Answer: B

Correct answer: 54

The terms shrink by a constant factor rather than by a constant amount: 4374 over 1458 is 3, and the same holds for every neighbouring pair, so each term is the previous one divided by 3. Dividing the last term, 162 over 3 is 54. As a check, multiplying the answer by 3 returns 162, the term before it. The terms of a halving series must eventually reach a number that will not divide evenly, which limits how long such a series can run.