Series Pattern Analysis

The given number series is: 10, 20, 11, 22, 14, 26, 19, 32, ?

This series can be analyzed by splitting it into two alternating sub-series:

• Odd-positioned terms: 10, 11, 14, 19, ?
• Even-positioned terms: 20, 22, 26, 32

Odd Position Terms Progression

Let's examine the pattern in the odd-positioned terms:

• 1st term: 10
• 3rd term: 11 (Difference: $11 - 10 = +1$)
• 5th term: 14 (Difference: $14 - 11 = +3$)
• 7th term: 19 (Difference: $19 - 14 = +5$)

The differences between consecutive odd terms are increasing odd numbers (1, 3, 5). The next difference should be 7.

Therefore, the next odd-positioned term (the 9th term) is calculated as:

$19 + 7 = 26$

Even Position Terms Progression

Let's examine the pattern in the even-positioned terms:

• 2nd term: 20
• 4th term: 22 (Difference: $22 - 20 = +2$)
• 6th term: 26 (Difference: $26 - 22 = +4$)
• 8th term: 32 (Difference: $32 - 26 = +6$)

The differences between consecutive even terms are increasing even numbers (2, 4, 6). The next difference would be 8.

The next even-positioned term (the 10th term) would be $32 + 8 = 40$.

Determining the Missing Number

The question mark is at the 9th position, which is an odd position.

Based on the pattern identified for the odd-positioned terms, the missing number is 26.