15, 60, 135, 240, ?

Concept: A number series can follow a quadratic pattern, where each term equals a fixed constant multiplied by the square of the term's position, rather than a simple constant-difference (arithmetic) progression. Such a pattern is confirmed by checking that the first differences between consecutive terms are not constant, but the differences of those differences (the second differences) are constant — the hallmark of an n2-based series.

Application:

1. List the position of each given term: 15 is the 1st term, 60 the 2nd, 135 the 3rd, and 240 the 4th; the missing value is the 5th term.

2. Find the first differences between consecutive terms: 60 − 15 = 45, 135 − 60 = 75, 240 − 135 = 105.

3. Find the second differences: 75 − 45 = 30 and 105 − 75 = 30 — constant, which confirms a quadratic (n2) pattern rather than a linear one.

4. Express each term as 15 × (position)2: 15×12=15, 15×22=60, 15×32=135, 15×42=240 — this matches every given term exactly.

5. Apply the same rule to the 5th position: 15 × 52 = 15 × 25 = 375.

Cross-check: Extending the difference pattern independently confirms this — continuing the constant second difference gives the next first difference as 105 + 30 = 135, so the next term is 240 + 135 = 375, matching the value obtained above.

So the missing term is 375.