# How do you write the expression for the nth term of the geometric sequence a_1=100, r=e^x, n=9?

Aug 4, 2018

${n}^{t h} t e r m = {a}_{n} = 100 {\left({e}^{x}\right)}^{n - 1}$
But
${9}^{t h} t e r m = {a}_{9} = 100 {\left({e}^{x}\right)}^{8}$

#### Explanation:

The ${n}^{t h}$term of the geometric sequence is :

color(blue)(a_n=a_1(r)^(n-1)

Given that ,

${a}_{1} = 100 , r = {e}^{x} \mathmr{and} n = 9$

$\therefore {n}^{t h} t e r m = {a}_{n} = 100 {\left({e}^{x}\right)}^{n - 1}$

$\therefore {9}^{t h} t e r m = {a}_{9} = 100 {\left({e}^{x}\right)}^{9 - 1} = 100 {\left({e}^{x}\right)}^{8}$