Complete the number series: 11, 12.2, 14.6, 18.2, ?

Introduction / Context:
This decimal number series features differences that themselves form a simple arithmetic progression. Candidates are expected to recognise the changing increments and use them to compute the next term. The given sequence is 11, 12.2, 14.6, 18.2, and we must find the next number.

Given Data / Assumptions:
- Sequence: 11, 12.2, 14.6, 18.2, ?- Values are positive decimal numbers.- Only one term at the end is missing.

Concept / Approach:
We begin by computing the differences between consecutive terms and then check whether those differences themselves form a simple pattern. Here, because we are working with tenths, we expect differences like 1.2, 2.4 and 3.6, which might form a clear arithmetic progression. Once that progression is identified, extending it by one more step will give the next difference and the next term in the series.

Step-by-Step Solution:
- From 11 to 12.2: 12.2 - 11 = 1.2.- From 12.2 to 14.6: 14.6 - 12.2 = 2.4.- From 14.6 to 18.2: 18.2 - 14.6 = 3.6.- Thus, the consecutive differences are 1.2, 2.4, 3.6.- These values form an arithmetic progression with common difference 1.2.- Therefore, the next difference should be 3.6 + 1.2 = 4.8.- The next term is then 18.2 + 4.8 = 23.0.- So, the required number is 23.

Verification / Alternative check:
- Reconstruct the sequence with the identified rule: 11 (+1.2) = 12.2, (+2.4) = 14.6, (+3.6) = 18.2, (+4.8) = 23.- The series of differences, 1.2, 2.4, 3.6, 4.8, is perfectly regular and supports our answer.

Why Other Options Are Wrong:
- 21.8, 24.6, 25 and 22.8 do not correspond to adding 4.8 to 18.2.- Using any of them would break the neat arithmetic progression in the differences.

Common Pitfalls:
- Miscalculating decimal differences and confusing 1.2 with 1.02 or 0.12.- Assuming a constant difference and stopping after noticing that the differences are not the same, rather than checking how they change.- Rounding intermediate steps carelessly can distort the underlying pattern.

Final Answer:
The differences increase by 1.2 each time, so the next difference is 4.8 and the next term is 18.2 + 4.8 = 23.