WAEC 2023 · Paper 1 · Q38

An exponential sequence (G.P.) is given by $8\sqrt{2}, 16\sqrt{2}, 32\sqrt{2}, \ldots$ . Find the $n^{\text{th}}$ term of the sequence.

Worked solution (try it first)

The first term is $a = 8\sqrt{2}$ and the common ratio is $r = \frac{16\sqrt{2}}{8\sqrt{2}} = 2$ .
The $n$ th term is $ar^{n - 1} = 8\sqrt{2} \times 2^{n - 1}$ .
Write 8 as $2^3$ : $2^3 \times 2^{n - 1} = 2^{n + 2}$ , so the $n$ th term is $2^{(n + 2)}\sqrt{2}$ , option D.