Show that the sequence is geometric.

MATHEMATICS · Multi-part · A Level · Mathematics · Sequences and series · Sequences and series

Problem

1. Show that the sequence

8, 4\sqrt{2}, 4, 2\sqrt{2}, \dots

is geometric. (1) Show that the sequence

8, 4\sqrt{2}, 4, 2\sqrt{2}, \dots

is geometric. (2) Hence show that the general term of the sequence is

u_n = 2^{\frac{7}{2} - \frac{1}{2}n}