Which of the following numbers will replace the question mark (?) in the given series?
$$9,20,42,86,174,?$$

Let us test the relationship between each consecutive term in the given number series:
* $$9\times 2+2=18+2=20$$

* $$20\times 2+2=40+2=42$$

* $$42\times 2+2=84+2=86$$

* $$86\times 2+2=172+2=174$$

The mathematical sequence logic multiplies each term by $2$ and adds $2$ to get the next term:

$$\text{Next Term}=(\text{Current Term}\times 2)+2$$

Applying this to find the missing term:

$$\text{Missing Term}=(174\times 2)+2=348+2=350$$

Thus, the required number is 350.