Suppose is an arithmetic sequence.

MATHEMATICS · Multi-part · CBSE · Mathematics · Sequences and Series · Sequences and Series

Problem

Suppose

u_1, u_2, u_3, \dots

is an arithmetic sequence. (a) Show that

2^{u_1}, 2^{u_2}, 2^{u_3}, \dots

is a geometric sequence. (b) Given that

u_3 = -4

and

u_5 = -10

, find the sum of the infinite geometric series

2^{u_1} + 2^{u_2} + 2^{u_3} + \dots