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

Concept: In a number series where every term is a perfect square, first take the square root of each term to recover the underlying sequence of bases. If the gaps between consecutive bases follow their own fixed pattern (for instance, doubling at each step, i.e. a geometric progression), that pattern predicts the next base - and squaring it gives the next term - even though the squared terms themselves are not in AP or GP.

1. Take the square root of each given term: √16 = 4, √36 = 6, √100 = 10, √324 = 18. So the bases are 4, 6, 10, 18.

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

3. These differences (2, 4, 8) double at every step, forming a geometric progression with common ratio 2, so the next difference is 8 × 2 = 16.

4. Add this difference to the last base: 18 + 16 = 34, which is the next base in the sequence.

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

Cross-check: 1156 is a perfect square (342), consistent with every other term in the series being a perfect square, and the base sequence 4, 6, 10, 18, 34 preserves the doubling pattern in its consecutive differences (2, 4, 8, 16) throughout - independently confirming the result.