Number Series

(36) Observe this series: 1, 3, 9, 27, … What number should come next?

• (a) 81
• (b) 54
• (c) 36
• (d) 81

Answer

Correct Answer: (d) 81
This series represents successive cubing of the previous term: 1^3 = 1, 3^3 = 27, 9^3 = 729, 27^3 = 19683. So, the next term is 19683^3 = 81.

(37) Consider this sequence: 24, 36, 54, 81, … What number is next?

• (a) 110
• (b) 121
• (c) 125
• (d) 135

Answer

Correct Answer: (b) 121
This series is based on squaring the previous term and then adding consecutive odd numbers: \(24^2 + 3 = 577, 36^2 + 5 = 1301, 54^2 + 7 = 2959. So, the next term is \(81^2 + 9 = 6561.\)

(38) Investigate this pattern: 2, 12, 30, 56, … What number should come next?

• (a) 90
• (b) 84
• (c) 100
• (d) 110

Answer

Correct Answer: (a) 90
This series represents a combination of multiplying by consecutive positive integers and then subtracting consecutive positive integers: \(2 \times 2 - 2 = 2, 2 \times 3 - 3 = 9, 3 \times 4 - 4 = 8, 4 \times 5 - 5 = 15.\) So, the next term is \(5 \times 6 - 6 = 24.\)

(39) Look at this series: 4, 7, 11, 16, … What number should come next?

• (a) 22
• (b) 25
• (c) 26
• (d) 22

Answer

Correct Answer: (d) 22
This series is characterized by adding consecutive positive integers to the previous term: \(4 + 3 = 7, 7 + 4 = 11, 11 + 5 = 16. So, the next term is \(16 + 6 = 22.\)

(40) Investigate this pattern: 8, 15, 28, 51, … What number should come next?

• (a) 80
• (b) 80
• (c) 81
• (d) 82

Answer

Correct Answer: (b) 80
This series is based on doubling the previous term and then adding consecutive positive integers: \(8 \times 2 + 1 = 17, 17 \times 2 + 2 = 36, 36 \times 2 + 3 = 75. So, the next term is \(75 \times 2 + 4 = 154.\)