Number Series

(41) Examine this series: 12, 9, 6, 3, … What number should come next?

• (a) 0
• (b) 1
• (c) 2
• (d) 0

Answer

Correct Answer: (d) 0
This series represents a decreasing pattern by subtracting 3 from the previous term: 12 - 3 = 9, 9 - 3 = 6, 6 - 3 = 3. So, the next term is 3 - 3 = 0.

(42) Investigate this pattern: 2, 4, 8, 16, … What number should come next?

• (a) 32
• (b) 24
• (c) 64
• (d) 32

Answer

Correct Answer: (d) 32
This series is characterized by doubling the previous term: 2 \times 2 = 4, 4 \times 2 = 8, 8 \times 2 = 16. So, the next term is 16 \times 2 = 32.

(43) Consider this sequence: 10, 14, 19, 25, … What number is next?

• (a) 32
• (b) 32
• (c) 33
• (d) 36

Answer

Correct Answer: (b) 32
This series is based on adding consecutive positive integers to the previous term: 10 + 4 = 14, 14 + 5 = 19, 19 + 6 = 25. So, the next term is 25 + 7 = 32.

(44) Investigate this pattern: 5, 12, 27, 58, … What number should come next?

• (a) 125
• (b) 128
• (c) 130
• (d) 135

Answer

Correct Answer: (a) 125
This series represents consecutive cubing of the previous term and then subtracting consecutive positive integers: \(5^3 - 1 = 124, 12^3 - 2 = 170, 27^3 - 3 = 19650, 58^3 - 4 = 196466.\) So, the next term is \(125^3 - 5 = 1953125.\)

(45) Look at this series: 7, 17, 37, 77, … What number should come next?

• (a) 147
• (b) 157
• (c) 167
• (d) 177

Answer

Correct Answer: (b) 157
This series is based on doubling the previous term and then adding 3: \(7 \times 2 + 3 = 17, 17 \times 2 + 3 = 37, 37 \times 2 + 3 = 77. So, the next term is \(77 \times 2 + 3 = 157.\)