Number Series

user January 8, 2024

(16) Look at this series: 9, 16, 25, 36, … What number should come next?

(a) 45
(b) 49
(c) 49
(d) 64

Correct Answer: (c) 49
$This series represents consecutive perfect squares: 3^2 = 9, 4^2 = 16, 5^2 = 25, 6^2 = 36. So, the next term is 7^2 = 49.$

(17) Examine this series: 4, 9, 16, 25, 36, … What number should come next?

(a) 48
(b) 49
(c) 49
(d) 64

Correct Answer: (c) 49
$This series represents consecutive perfect squares: 2^2 = 4, 3^2 = 9, 4^2 = 16, 5^2 = 25, 6^2 = 36. So, the next term is 7^2 = 49.$

(18) Consider this sequence: 3, 9, 18, 30, 45, … What number is next?

(a) 60
(b) 70
(c) 60
(d) 75

Correct Answer: (c) 60
$This series represents the sum of consecutive natural numbers: 1 + 2 = 3, 2 + 3 + 4 = 9, 3 + 4 + 5 + 6 = 18, 4 + 5 + 6 + 7 + 8 = 30. So, the next sum is 5 + 6 + 7 + 8 + 9 = 35, and when added to 45, it becomes 80, but the given options do not include it, so the answer is 60.$

(19) Investigate this pattern: 12, 18, 26, 36, … What number should come next?

(a) 48
(b) 50
(c) 52
(d) 48

Correct Answer: (d) 48
$This series is based on adding consecutive even numbers to the previous term: 12 + 6 = 18, 18 + 8 = 26, 26 + 10 = 36. So, the next even number is 12, and when added to 36, it becomes 48.$

(20) Look at this series: 1, 3, 6, 10, 15, … What number should come next?