# How do you find a_9 for the geometric sequence 60, 30, 15, ...?

Nov 24, 2016

See explanation.

#### Explanation:

First we have to find the sequence's first term (${a}_{1}$) and common quotient ($q$).

First term is ${a}_{1} = 60$

Quotient is $q = {a}_{2} / {a}_{1} = \frac{30}{60} = \frac{1}{2}$

Now to find the nineth term we can use:

${a}_{9} = {a}_{1} \times {q}^{8} = 60 \times {\left(\frac{1}{2}\right)}^{8} = \frac{60}{128} = \frac{15}{32}$