Question

in the following geometric sequence, find (i) the 7th term; (ii) the nth term:-1/3, 3/4, -9/8, .....

Answer 1

Given the geometric sequence:

$-\frac{1}{2},\frac{3}{4},\frac{-9}{8},\ldots.$

The common ratio will be:

$r=\frac{3}{4}\div-\frac{1}{2}=\frac{3}{4}\cdot-2=-\frac{3}{2}$

The general rule of the geometric sequence will be:

$a_n=a_1\cdot r^{n-1}$

so, a7 will be:

$a_7=-\frac{1}{2}\cdot(-\frac{3}{2})^{7-1}=-\frac{1}{2}\cdot(-\frac{3}{2})^6=-\frac{729}{128}$

And an will be:

$a_n=(-\frac{1}{2})\cdot(-\frac{3}{2})^{n-1}_{}$