Question

Find the explicit formula for the geometric sequence. Then find a8. 4, 8, 16, 64, ...

Answer 1

The given sequence is : 4,8, 16,64

The geometric series is exoress as :

`\text{ Geometric series=a, ar, ar}^2\ldots.ar^n`

where r i the common ratio

In the given sequence the ratio is

`\begin{gathered} r=\frac{\sec ond\text{ term}}{first\text{ term}} \\ r=(8)/(4) \\ r=2 \end{gathered}`

So, the series will express as :

`\begin{gathered} \text{Explict formula = 4(2)}^(n-1) \\ \text{Explict form = }4(2)^(n-1) \end{gathered}`

Now for the 8 term

n=8

`\begin{gathered} a_n=4\cdot2^(n-1) \\ a_8=4\cdot2^(8-1) \\ a_8=4\cdot2^7 \\ a_8=512 \end{gathered}`

Answer : C) an=4.2^n-1, 512