What will come in the place of question (?) mark in the following number…

Concept

In a number series, when the gaps between consecutive terms keep growing, examine the differences as a pattern of their own. A common construction makes each successive difference equal to the square of the next odd number plus a fixed constant, so the gaps themselves grow in a predictable way.

Application

Find the differences between consecutive terms, then describe those differences:

1. 66 − 40 = 26, and 26 = 52 + 1.

2. 116 − 66 = 50, and 50 = 72 + 1.

3. 198 − 116 = 82, and 82 = 92 + 1.

4. 320 − 198 = 122, and 122 = 112 + 1.

The added odd numbers run 5, 7, 9, 11, so the next one is 13. The next difference is therefore 132 + 1 = 169 + 1 = 170.

Add this to the last term: 320 + 170 = 490.

Cross-check

A second independent view confirms it: list the second-level differences of 26, 50, 82, 122, which are 24, 32, 40 — an arithmetic run rising by 8. The next second-level difference is 40 + 8 = 48, so the next first-level difference is 122 + 48 = 170, and 320 + 170 = 490 again. Both routes agree, so the missing term is 490.