What will come in the place of question (?) mark in the following number series.

32, 40, 53, 76, ?, 172

The correct option is 114.

To find the missing number in the given series, let us analyze the differences between consecutive terms:

Difference between 1^st and 2^nd term:

40 - 32 = 8

Difference between 2^nd and 3^rd term:

53 - 40 = 13

Difference between 3^rd and 4^th term:

76 - 53 = 23

Now, let us examine the sequence of differences obtained so far: 8, 13, 23, ...

Let us look at the differences of these differences (the second-order difference):

13 - 8 = 5

23 - 13 = 10

We can observe that the second-order difference increases by multiples of 5 (5, 10, 15, 20, ...):

Next second-order difference should be 15.

Therefore, the next difference to add to 76 will be:

23 + 15 = 38

Adding 38 to the 4^th term (76) gives the missing number (?):

76 + 38 = 114

To verify, let us calculate the next step:

The next second-order difference would be 20.

The next term difference will be: 38 + 20 = 58.

Adding 58 to 114 gives: 114 + 58 = 172, which matches the final number in the series.

Hence, the missing number in place of the question mark (?) is 114.