Find the missing term that replaces the question mark (?) in the given numerical sequence.

35, 72, 113, ?, 203, 256, 315

The correct answer is 156.

To find the missing term that replaces the question mark (?) in the given numerical sequence, we analyze the pattern by calculating the differences between consecutive terms.

Given sequence: 35, 72, 113, ?, 203, 256, 315

Let us calculate the differences between the known adjacent terms:

$72-35=37$

$113-72=41$

$256-203=53$

$315-256=59$

Notice the sequence of differences: 37, 41, ?, ?, 53, 59.

The numbers 37, 41, 53, and 59 are consecutive prime numbers. The prime numbers that lie between 41 and 53 are 43 and 47.

Thus, the pattern of differences consists of consecutive prime numbers: 37, 41, 43, 47, 53, 59.

To find the missing term, add the next prime number (43) to the term preceding the question mark (113):

$\text{Missing term}=113+43=156$

We can verify this result by adding the subsequent prime number (47) to 156:

$156+47=203$

This matches the next term in the sequence (203), confirming that the missing term is indeed 156.