In a geometric progression

MATHEMATICS · Single correct · A Level · Mathematics · Sequences and series · Sequences and series

Problem

In a geometric progression, the first term is

6

and the common ratio is

3

. If

T_k

denotes its

k

-th term, what is the value of

T_1+T_3+T_5+\cdots+T_{2n-1}

, the sum of the odd-numbered terms among the first

2n

terms? (a)

\dfrac{3}{4}\bigl(3^{2n}-1\bigr)

(b)

\dfrac{3}{4}\bigl(9^{n}-1\bigr)

(c)

3\bigl(3^{n}-1\bigr)

(d)

\dfrac{3}{4}\bigl(9^{2n}-1\bigr)