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

The correct answer is 350.

To find the number that replaces the question mark (?) in the given series: 9, 20, 42, 86, 174, ?, we can analyze the relationship between consecutive terms.

Method 1: Multiply by 2 and add 2

Each term in the series is obtained by multiplying the preceding term by 2 and adding 2:

$9\times 2+2=18+2=20$
$20\times 2+2=40+2=42$
$42\times 2+2=84+2=86$
$86\times 2+2=172+2=174$

Following the exact same pattern for the next number:

$174\times 2+2=348+2=350$

Method 2: Difference pattern

Alternatively, we can examine the differences between successive numbers in the series:

$20-9=11$
$42-20=22$ (which is $11\times 2$)
$86-42=44$ (which is $22\times 2$)
$174-86=88$ (which is $44\times 2$)

The difference doubles at each step. Therefore, the next difference to add is:

$88\times 2=176$

Adding 176 to the last given term (174) yields:

$174+176=350$

Hence, the number that replaces the question mark (?) is 350.