Consider the series given below. Find the number to be inserted in place of the question mark: 5, 14, 39, 88, 209, ?, 667

A378 ✓ Correct

B297

C299

D375

Correct answer: (A) 378

Explanation

The missing number is 378.

The differences are squares of successive primes: 3, 5, 7, 11, 13, 17.

5 + 9 = 14, 14 + 25 = 39, 39 + 49 = 88, 88 + 121 = 209.

The next difference is 13^2 = 169, so 209 + 169 = 378.

Check: 378 + 17^2 = 378 + 289 = 667.

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