Number Series

(11) Examine this series: 5, 8, 13, 20, … What number should come next?

• (a) 30
• (b) 29
• (c) 26
• (d) 35

Answer

Correct Answer: (b) 29
This series represents consecutive prime numbers incremented by 1: 5 (prime) + 1 = 6, 8 (prime) + 1 = 9, 13 (prime) + 1 = 14, 20 (prime) + 1 = 21, so the next prime number is 29 (21 + 1 = 22, 23, 24, 25, 26, 27, 28, 29).

(12) Observe the following sequence: 1, 4, 9, 16, 25, … What number comes next?

• (a) 36
• (b) 30
• (c) 49
• (d) 56

Answer

Correct Answer: (a) 36
This series represents consecutive perfect squares: 1 = 1^2, 4 = 2^2, 9 = 3^2, 16 = 4^2, 25 = 5^2. So, the next term is 36 = 6^2.

(13) Consider this sequence: 2, 4, 8, 16, 32, … What number is next?

• (a) 48
• (b) 64
• (c) 36
• (d) 64

Answer

Correct Answer: (d) 64
This series is based on doubling the previous number: 2 \times 2 = 4, 4 \times 2 = 8, 8 \times 2 = 16, 16 \times 2 = 32, 32 \times 2 = 64.

(14) Investigate this pattern: 3, 7, 15, 31, … What number should come next?

• (a) 59
• (b) 63
• (c) 67
• (d) 71

Answer

Correct Answer: (b) 63
This series is characterized by doubling the previous number and then adding 1: 3 \times 2 + 1 = 7, 7 \times 2 + 1 = 15, 15 \times 2 + 1 = 31, so 31 \times 2 + 1 = 63.

(15) Look at this series: 1, 2, 6, 24, … What number should come next?

• (a) 120
• (b) 72
• (c) 48
• (d) 96

Answer

Correct Answer: (a) 120
This series is based on multiplying the previous number by the next positive integer: 1 \times 2 = 2, 2 \times 3 = 6, 6 \times 4 = 24, so 24 \times 5 = 120.