# Write an expression for the nth term of the geometric sequence. Then find the indicated term. a_1...

## Question:

Write an expression for the nth term of the geometric sequence. Then find the indicated term.

{eq}a_1 = 4, r = \frac{1}{6}, n = 10 {/eq}

## Geometric Sequence:

Recall that a geometric sequence is one that is made by constantly multiplying by a number. We call the number we keep multiplying by {eq}r {/eq} (for "repeat" maybe?), and in general we call the {eq}n {/eq}th term {eq}a_n {/eq}, so that {eq}a_1 {/eq} is the first term in the sequence. Then, the general formula to find the {eq}n {/eq}th term in a geometric sequence is

{eq}\begin{align*} a_n &= a_1 r^{n-1} \end{align*} {/eq}

## Answer and Explanation: 1

Our first term is {eq}a_1 {/eq} is 4, and the number we want to multiply by "r"epeatedly is {eq}r = \frac16 {/eq}. So the {eq}n {/eq}th term in the sequence is given by

{eq}\begin{align*} a_n &= 4 \left( \frac16 \right)^{n-1} \end{align*} {/eq}

Then the 10th term in the sequence (i.e. {eq}a_n {/eq} when {eq}n = 10 {/eq}) is

{eq}\begin{align*} a_{10} &= 4 \left( \frac16 \right)^{10-1} \\ &= \frac{4}{6^9} \\ &= \frac1{2519424} \end{align*} {/eq}

which by most practical accounts would be considered 0.

#### Learn more about this topic:

from

Chapter 21 / Lesson 8A geometric sequence can be identified by its specific common ratio. Learn about the definition of a geometric sequence, how to find the common ratio, how to continue a geometric sequence, and explore several examples of geometric sequences.