Multiple choice

Select the missing term from the given alternatives to complete the series. $1, 5, 21, 57, 121, 221, ?$

  1. $278$
  2. $342$
  3. $256$
  4. $365$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Analyze the differences between consecutive terms: 5-1=4, 21-5=16, 57-21=36, 121-57=64, 221-121=100. The differences are 4, 16, 36, 64, 100 - which are squares of even numbers: 2^2, 4^2, 6^2, 8^2, 10^2. Following this pattern, the next difference should be 12^2 = 144. Therefore, the next term is 221 + 144 = 365. Option D is correct.

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