Question

The 5th term of a geometric sequence is 45 and the 8th term is 360. How do you determine the 20th term?

Answer 1

`1474560`

Explanation:

First we need to find the ratio, `r` and the first term:`a`.
We know that `a*r^5=45` and `a*r^8=360`.

To determine `r` can divide the 8th term by the 5th term like so:

`(ar^8)/(ar^5)=360/45`

The `a`s will cancel and the rest will simplify to:

`r^3=8`
`-> r =2`

To find `a` simply substitute `r` into either of the known terms, i.e:

`a*2^5=45-> a=45/2^5=45/32`

Now we can find the twentieth term:

`ar^20=45/32*2^20=1474560`