Question

How do you use the geometric sequence formula to find the nth term?

Answer 1

A geometric sequence is always of the form
`t_n=t_"n-1"*r`

Every next term is `r` times as large as the one before.

So starting with `t_0` (the "start term") we get:
`t_1=r*t_0`
`t_2=r*t_1=r*r*t_0=r^2*t_0`
......
`t_n=r^n*t_0`

Answer:
`t_n=r^n*t_0`
`t_0` being the start term, `r` being the ratio

Extra:
If `r>1` then the sequence is said to be increasing
if `r=1` then all numbers in the sequence are the same
If `r<1` then the sequence is said to be decreasing ,
and a total sum may be calculated for an infinite sequence:
sum `sum=t_0/(1-r)`

Example :
The sequence `1,1/2,1/4,1/8...`
Here the `t_0=1` and the ratio `r=1/2`
Total sum of this infinite sequence:
`sum=t_0/(1-r)=1/(1-1/2)=2`