50, 60, 80, 105, 132.5, ?
Find the missing number in the following number series.

The correct option is 161.25.

Let us analyze the pattern behind the given number series:
50, 60, 80, 105, 132.5, ?

First, calculate the differences between consecutive terms in the series:

$60-50=10$

$80-60=20$

$105-80=25$

$132.5-105=27.5$

Now, let us examine the pattern in the differences: 10, 20, 25, 27.5.

Notice how each successive difference is generated from the previous difference:

Second difference: $10+\frac{10}{1}=20$ (or $10+10=20$)

Third difference: $20+\frac{10}{2}=20+5=25$

Fourth difference: $25+\frac{10}{4}=25+2.5=27.5$

Following this sequence, the added value to the previous difference is halved at each step ($10$, then $5$, then $2.5$). Therefore, the next addition to the difference will be $\frac{2.5}{2}=1.25$.

Fifth difference: $27.5+1.25=28.75$

Now, add this fifth difference to the last term of the given series to find the missing number (?):

$?=132.5+28.75=161.25$

Thus, the missing number in the series is 161.25.