# How do you write the expression for the nth term of the geometric sequence a_1=5, r=3/2, n=8?

Apr 29, 2018

${a}_{n} = 5 {\left(\frac{3}{2}\right)}^{n - 1}$

#### Explanation:

$\text{the n th term of a geometric sequence is}$

•color(white)(x)a_n=a_1r^(n-1)

$\text{here "a_1=5" and } r = \frac{3}{2}$

$\Rightarrow {a}_{n} = 5 {\left(\frac{3}{2}\right)}^{n - 1}$

$\Rightarrow {a}_{8} = 5 {\left(\frac{3}{2}\right)}^{7} = 5 \times \frac{2187}{128} = \frac{10935}{128}$