How do you write the expression for the nth term of the geometric sequence a_1=4, r=1/2, n=10?

Jul 5, 2017

See the explanation below.

Explanation:

The equation for a geometric sequence is ${a}_{n} = {a}_{1} {\left(r\right)}^{n - 1}$, where ${a}_{n}$ is the ${n}^{t h}$ term, ${a}_{1}$ is the first term, and $r$ is the common ratio.

We can substitute the given values into the equation.

${a}_{10} = 4 {\left(\frac{1}{2}\right)}^{10 - 1}$

${a}_{10} = 4 {\left(\frac{1}{2}\right)}^{9}$

${a}_{10} = 4 \left(\frac{1}{512}\right)$

${a}_{10} = \frac{1}{128}$