Consider the following series : 1, 9, 17, 33, 49, 73, … Identify the

Consider the following series :
1, 9, 17, 33, 49, 73, …
Identify the missing number from the following :

99
97
95
91
This question was previously asked in
UPSC CAPF – 2019
The given series is 1, 9, 17, 33, 49, 73, …
Let’s find the difference between consecutive terms:
9 – 1 = 8
17 – 9 = 8
33 – 17 = 16
49 – 33 = 16
73 – 49 = 24
The sequence of differences is 8, 8, 16, 16, 24. The pattern is that each difference appears twice, and the difference increases by 8 each time (8, then 8+8=16, then 16+8=24).
Following this pattern, the next difference should also be 24.
The missing number is the last term plus the next difference: 73 + 24 = 97.
– Analyze the differences between consecutive terms to find the underlying pattern.
– The differences form a sequence of paired numbers with a constant increment.
This is a type of second-order arithmetic progression where the differences between terms follow a pattern. Recognizing the sequence of differences (8, 8, 16, 16, 24, 24…) is key to solving the puzzle.