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

Let's examine the difference between consecutive terms of the sequence:
* $90-45=45$
* $154-90=64$

Let $x$ be the missing number replacing the question mark. Let's analyze the pattern by calculating the second differences (the differences between the differences):

* Difference between the first two differences $=64-45=19$

If the series follows a constant increase in differences by consecutive odd numbers ($19,21,23$), let's determine the next differences:

* The next difference should be: $64+21=85$
* Therefore, the missing term $x$ would be: $154+85=239$

Let's verify this pattern with the final term of the series:

* The subsequent difference should be: $85+23=108$
* The final term would be: $239+108=347$, which perfectly matches the given series.

Thus, the missing number is $239$.