A series is given with one term missing. Choose the correct alternative from the given options that will complete the series: 5, 7.5, 12.5, 22.5, ?

Introduction / Context:
This series uses decimal numbers and shows increasing differences between terms. The pattern is that the increment doubles at each step. Such problems test attention to decimal arithmetic and recognition of a simple relationship in the sequence of differences. The series is 5, 7.5, 12.5, 22.5, ?, and we must find the next term.

Given Data / Assumptions:
- Series: 5, 7.5, 12.5, 22.5, ?- The final term is missing.- All numbers are positive decimals.- Differences appear to grow rapidly, hinting at a doubling pattern.

Concept / Approach:
We compute consecutive differences between terms and examine how they change. If each difference is twice the previous one, then the next difference can be obtained by another doubling. This difference is then added to the last known term to obtain the missing number.

Step-by-Step Solution:
- Difference from 5 to 7.5: 7.5 - 5 = 2.5.- Difference from 7.5 to 12.5: 12.5 - 7.5 = 5.0.- Difference from 12.5 to 22.5: 22.5 - 12.5 = 10.0.- The differences are 2.5, 5, 10, which clearly double each time: 2.5 * 2 = 5, 5 * 2 = 10.- Therefore, the next difference should be 10 * 2 = 20.- Add this to the last known term: 22.5 + 20 = 42.5.- So the missing term is 42.5.

Verification / Alternative check:
- The full difference sequence becomes 2.5, 5, 10, 20, which is a geometric progression with ratio 2.- The reconstructed series 5, 7.5, 12.5, 22.5, 42.5 respects this doubling pattern exactly.- No alternative candidate preserves such a clean and simple progression of differences.

Why Other Options Are Wrong:
- 42, 44, 43.5 and 40.5 yield differences of 19.5, 21.5, 21 and 18 from 22.5, none of which equals 20, the expected next difference.- These values break the doubling rule for the increments and do not fit the geometric pattern in the differences.

Common Pitfalls:
- Rounding errors or misreading decimal points can cause miscalculation of differences like 2.5 or 10.- Some candidates look for a multiplicative rule for the main terms instead of examining differences, which is less natural in this particular series.- Ignoring the clear doubling pattern among differences may lead to random choice among the options.

Final Answer:
The differences double at each step (2.5, 5, 10, 20), so the missing term is 42.5.