Which number completes the given series?

6, 14, 30, 62, ?

The correct option is 126.

To find the missing number in the given sequence, let us analyze the relationship between consecutive numbers:

6, 14, 30, 62, ?

Let us look at how each term is obtained from the previous term:

First term = 6

Second term:

$6\times 2+2=12+2=14$

Third term:

$14\times 2+2=28+2=30$

Fourth term:

$30\times 2+2=60+2=62$

Following the same pattern, the missing fifth term is calculated by multiplying the previous term by 2 and adding 2:

$62\times 2+2=124+2=126$

Alternatively, we can look at the differences between consecutive terms:

14 - 6 = 8

30 - 14 = 16

62 - 30 = 32

Notice that each difference is twice the previous difference (8, 16, 32). Therefore, the next difference must be:

$32\times 2=64$

Adding this difference to the last known term gives:

$62+64=126$

Thus, the number that completes the series is 126.