Which is the n-th term of the series?

Correct answer: c 2 (3/√2)ⁿ⁻¹

a = 2, r = 3√2/2 = 3/√2; uₙ = 2 · (3/√2)ⁿ⁻¹; n = 2, 3, 4 give 3√2, 9, 27/√2.

Why the other options are wrong

• a (n + 1)√n: n = 3 gives 4√3, but the third term is 9; the formula fits the first two terms and breaks at the third.
• b 2n/2ⁿ⁻¹: n = 2 gives 4/2 = 2, but the second term is 3√2.
• d 2 · 2ⁿ/2ⁿ⁻¹: 2 · 2ⁿ/2ⁿ⁻¹ = 4 for every n, a constant; but the terms change.