Find the missing term in the following series: 2, 8, 16, 128, ?

In a multiplicative recursive series, each term from the third one onward is the product of the two terms immediately preceding it: T(n) = T(n−1) × T(n−2). Once this governing rule is identified, any missing term can be found directly from its two neighbours.

1. Third term = product of the first two terms: 2 × 8 = 16 — matches the given series.

2. Fourth term = product of the second and third terms: 8 × 16 = 128 — matches the given series.

3. Missing (fifth) term = product of the third and fourth terms: 16 × 128 = 2048.

Cross-check: dividing the found term by the term just before it should return the term before that — 2048 ÷ 128 = 16, exactly the third term, confirming the pattern holds consistently across the series.

So the missing term is 2048.