Mathematics

Problem

Let

\{a_n\}

be a GP with positive terms, first term

3

and common ratio

2

. A new sequence

\{T_n\}

is defined by

T_n = \dfrac{1}{5a_n}

for all

n \ge 1

. a. (i) Prove that

\{T_n\}

forms a GP and find its first term and common ratio. b. (ii) Obtain the sum of the first four terms of

\{T_n\}