16, 36, 100, 324, ? Find the next term.

Concept: In a number series built from perfect squares, the pattern often lives in how the bases (the numbers being squared) grow rather than in the raw terms. Write each term as a base squared, then examine the differences between consecutive bases: when those differences themselves form a geometric progression (each one a fixed multiple of the one before), extend that progression one more step to get the next base, then square it to get the next term.

Application:

1. Express every given term as a perfect square: 16 = 42, 36 = 62, 100 = 102, 324 = 182.

2. List the bases in order: 4, 6, 10, 18.

3. Find the differences between consecutive bases: 6 − 4 = 2, 10 − 6 = 4, 18 − 10 = 8.

4. These differences — 2, 4, 8 — form a geometric progression with common ratio 2 (21, 22, 23), so the next difference in the progression is 24 = 16.

5. Add that difference to the last base: 18 + 16 = 34.

6. Square the new base to get the next term: 342 = 1156.

Cross-check: Check the ratio stays constant across every step: 4 ÷ 2 = 2 and 8 ÷ 4 = 2, confirming the common ratio is exactly 2, so 8 × 2 = 16 is the correct next difference — and 34 × 34 = 1156 confirms the squaring.

So the next term in the series is 1156.