Consider the series given below. Find the number which can be inserted at the…

Concept

In a number series, inspect the differences between consecutive terms. A regular pattern in those differences can reveal the rule that generates the series.

When the differences are squares of consecutive prime numbers, add each prime square in order to obtain the next term.

Application

1. 14 − 5 = 9 = 32.

2. 39 − 14 = 25 = 52.

3. 88 − 39 = 49 = 72.

4. 209 − 88 = 121 = 112.

5. The next prime after 11 is 13, so the missing term is 209 + 132 = 209 + 169 = 378.

Cross-check

The following prime is 17, and 378 + 172 = 378 + 289 = 667, which reproduces the final given term.

Result

Therefore, the missing number is 378.