Directions: Find the missing term in the following number series.

?, 31, 27, 36, 20, 45

The correct answer is 32.

To find the missing term in the number series, we can analyze the pattern by splitting the series into two alternating sub-series (terms at odd positions and terms at even positions):

Given series:
?, 31, 27, 36, 20, 45

Even-positioned terms:
2nd term = 31
4th term = 36
6th term = 45

Let us check the differences for the even-positioned terms:

$31+5=36$

$36+9=45$

The difference increases by 4 (from +5 to +9).

Odd-positioned terms:
1st term = ?
3rd term = 27
5th term = 20

Let us check the difference between the 3rd and 5th terms:

$27-7=20$

Following the pattern of subtraction with consecutive odd numbers (5, 7), the difference between the 1st term (?) and the 3rd term (27) must be -5.

Let the missing term be represented by $x$.

$x-5=27$

$x=27+5$

$x=32$

Hence, the missing term in the series is 32.