Join 60,000+ competitive exam aspirants
or with email
Your Cart
Subtotal₹0
Total₹0
Examoogle • User • info@examoogle.com • EE-2024-8821
Chapter 1 of 12 • Page 1 of 248🔒 Protected PDF • Watermarked
Join 60,000+ competitive exam aspirants
What should come in place of ‘?’ in the given series? 8, 9, 13, 22, 38, 63,?
98
99
100
101
99
Observe the differences between consecutive terms; they follow a sequence of perfect squares: 1 squared, 2 squared, 3 squared, 4 squared, 5 squared, and 6 squared.
Observe the differences between consecutive terms; they follow a sequence of perfect squares: 1 squared, 2 squared, 3 squared, 4 squared, 5 squared, and 6 squared.
Analyze consecutive differences
Calculate the difference between each term: 9-8=1, 13-9=4, 22-13=9, 38-22=16, 63-38=25.
Identify the pattern
The differences are 1, 4, 9, 16, 25, which represent 1², 2², 3², 4², 5² respectively.
Calculate the next term
Following the pattern, the next difference must be 6² = 36. Add 36 to the last term: 63 + 36 = 99.
A: 98 is incorrect because the difference 35 is not a perfect square. C: 100 is incorrect because the difference 37 is not a perfect square. D: 101 is incorrect because the difference 38 is not a perfect square.
B is correct because the series follows an increment pattern of consecutive perfect squares (1, 4, 9, 16, 25, 36), resulting in 63 plus 36 equaling 99.
When a series grows at an increasing rate, always check the difference between consecutive numbers first; if the first layer of differences is not obvious, check the difference of the differences.