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 in the given number series step-by-step:

Series: 50, 60, 80, 105, 132.5, ?

First, let us calculate the difference between consecutive terms:

First difference: 60 - 50 = 10

Second difference: 80 - 60 = 20

Third difference: 105 - 80 = 25

Fourth difference: 132.5 - 105 = 27.5

Now, let us analyze the relation between these successive differences:

From 10 to 20: 10 × 2 = 20

From 20 to 25: 20 × 1.25 = 25

From 25 to 27.5: 25 × 1.1 = 27.5

Alternatively, let us observe the pattern of operations applied to each term to get the next term directly:

$50\times 1+10=60$

$60\times 1+20=80$

$80\times 1+25=105$

$105\times 1+27.5=132.5$

Looking at the differences added at each step:

10 = 10 × 1

20 = 10 × 2

25 = 20 × 1.25 = 10 × 2.5

27.5 = 25 × 1.1 = 10 × 2.75

The multipliers for 10 in the differences are: 1, 2, 2.5, 2.75, ...

The differences between these multipliers are: +1, +0.5, +0.25, ... (each increment is halved).

The next multiplier increment will be 0.125, making the next multiplier:

2.75 + 0.125 = 2.875

Therefore, the next difference to add is:

$10\times 2.875=28.75$

Adding this difference to the last known term (132.5):

$132.5+28.75=161.25$

Hence, the missing number in the series is 161.25.