Number Series

user January 8, 2024

(1) Look at this series: 2, 6, 18, 54, … What number should come next?

(a) 162
(b) 108
(c) 162
(d) 216

Correct Answer: (c) 162
$This is a simple multiplication series; each number is the previous number multiplied by 3. The pattern follows: 2 \times 3 = 6, 6 \times 3 = 18, 18 \times 3 = 54, 54 \times 3 = 162.$

(2) Observe this pattern: 5, 11, 19, 29, 41, … What number should come next?

(a) 53
(b) 55
(c) 61
(d) 65

Correct Answer: (b) 55
$This series is characterized by prime numbers increasing by the next even number: 5 + 6 = 11, 11 + 8 = 19, 19 + 10 = 29, 29 + 12 = 41, 41 + 14 = 55.$

(3) Consider this sequence: 3, 4, 8, 17, 33, … What number is next?

(a) 58
(b) 60
(c) 64
(d) 58

Correct Answer: (d) 58
$The sequence adds consecutive prime numbers to the previous term: 3 + 1 = 4, 4 + 4 = 8, 8 + 9 = 17, 17 + 16 = 33, 33 + 25 = 58.$

(4) Examine this series: 10, 20, 40, 80, … What number should come next?

(a) 160
(b) 140
(c) 100
(d) 120

Correct Answer: (a) 160
$This series is a simple multiplication pattern; each number is double the previous one. The pattern follows: 10 \times 2 = 20, 20 \times 2 = 40, 40 \times 2 = 80, 80 \times 2 = 160.$

(5) Analyze this sequence: 1, 3, 6, 10, 15, … What number comes next?