Question

The question is: type your equation for the following pattern

the chart is
x.y
___
1. | 16.
2.| 8.
3.| 4.
4.| 2.
5.| 1.
please show your work!

Answer 1

`\large\boxed{a(n)=16\left((1)/(2)\right)^(n-1)}`

Explanation:

`a(1)=16\\\\a(2)=16:2=8\\\\a(3)=8:2=4\\\\a(4)=4:2=2\\\\a(5)=2:2=1\\\\a(n)=a_(n-1):2=(1)/(2)a_(n-1)`

This is a geometric series with the common ratio
`r=(1)/(2)` and the first term
`a_1=16`.

An explicit formula of the n-th term of a geometric sequence:

`a_n=a_1r^(n-1)`

Substitute:

`a_n=16\left((1)/(2)\right)^(n-1)`