Look at this series: 1.5, 2.3, 3.1, 3.9, ... What number should come next?

Concept: An arithmetic progression (AP) is a sequence in which the difference between any two consecutive terms stays the same constant value, called the common difference. To extend such a series, first find this common difference from the given terms, then add it to the last known term.

Application:

1. Find the difference between each pair of consecutive terms: 2.3 − 1.5 = 0.8; 3.1 − 2.3 = 0.8; 3.9 − 3.1 = 0.8.

2. Every difference equals 0.8, so the series has a constant common difference of 0.8, confirming it is an arithmetic progression.

3. Add the common difference to the last given term: 3.9 + 0.8 = 4.7.

Cross-check: Using the general term formula for an AP, an = a1 + (n − 1)d, with a1 = 1.5, d = 0.8, and n = 5: a5 = 1.5 + 4(0.8) = 1.5 + 3.2 = 4.7 — confirming the result.