Question 0403a

Arithmetic and Geometric Progressions (APs, GPs)

Sums and Terms

Question

The sum of the first

{n}

terms of a series is given by

S_n = 2^n - 1.

An expression for the

{n\textrm{th}}

term of the series,

{u_n,}

can be expressed in the form

\displaystyle u_n = p q^n,

where

{p}

and

{q}

are rational numbers. Find

{p}

and

{q.}

{p=}

{q=}