Which of the following numbers will replace the question mark (?) in the given series?
45, 90, 154, ?, 347

The correct answer is 239.

Let us analyze the logical pattern in the given number series:
45, 90, 154, ?, 347

First, we examine the differences between consecutive terms in the series:

1st difference: $90-45=45$

2nd difference: $154-90=64$

Now, let us examine the pattern in the differences themselves (45, 64, ...):

Notice how the differences relate to consecutive squares:
$7^2-4=49-4=45$
$8^2-0=64-0=64$

Alternatively, looking at the second-level difference (the difference of differences):
$64-45=19$

If the second-level difference increases by 2 each step (19, 21, 23):

3rd difference: $64+21=85$

Adding this 3rd difference to the 3rd term (154):
$154+85=239$

To verify, let us calculate the 4th difference using the same pattern:
4th difference: $85+23=108$

Adding this to 239:
$239+108=347$

This matches the final term (347) given in the series.

Therefore, the number that replaces the question mark (?) is 239.