What number should replace question mark (?) in the series given below? 7, 10, 19, 46, 127?

The correct option is 370.

To find the missing number in the given series, let us analyze the differences between consecutive terms:
First term = 7
Second term = 10
Third term = 19
Fourth term = 46
Fifth term = 127

Let us calculate the differences between adjacent terms:
Difference between 1st and 2nd term: 10 - 7 = 3
Difference between 2nd and 3rd term: 19 - 10 = 9
Difference between 3rd and 4th term: 46 - 19 = 27
Difference between 4th and 5th term: 127 - 46 = 81

If we look closely at the sequence of differences (3, 9, 27, 81), we can see that each difference is a power of 3:

$3^1=3$

$3^2=9$

$3^3=27$

$3^4=81$

Following this pattern, the next difference in the series must be 3 raised to the power of 5:

$3^5=243$

Therefore, we find the next number in the series by adding this difference to the last term (127):
Missing number = 127 + 243 = 370