Question

How do you identify 19th term of a geometric sequence where a1 = 14 and a9 = 358.80?

Answer 1

An explanation is given below.

Explanation:

We are to find `19`th term of Geometric Sequence
Given `a_1 = 14` and `a_9 = 358.80`

The general term of a Geometric Sequence is given by

`a_n = a*r^(n-1)`
Where `a` is the first term also known as `a_1` and `r` is the common ratio.

We have `a_1` if we get `r` we can easily find `a_19` by using `19` for `n`

Let us start by writing the given term using `r`

`a_9 = a*r^8`

If we divide `a_9` by `a_1` we would get an equation in `r`

`(ar^8)/(a) = 358.80/14`

`r^8 = 25.628571428571428571428571428571`
Taking `8`th root.

`r=root(8)(25.628571428571428571428571428571)`
#r=1.4999975504465127405341330547934"

`r~~ 1.5`

`a_19 = 14(1.5)^19`

`a_19 = 31,035.729480743408203125"`
`a_19 ~~ 31035.73`