Question

Given two terms in a geometric sequence, find the common ratio. Please helpp

Answer 1

In a geometric sequence, consecutive terms have a common ratio:

`(a_(n+1))/(a_n)=r\quad \forall n\geq 1`

This means that, in order to build a gometric sequence, we must choose an initial value
`a_1` and a common ratio
`r`, and we'll multiply each term by
`r` to get the next one:

`a_1=a_1`

`a_2=ra_1`

`a_3=r^2a_1`

`a_4=r^3a_1`

`a_5=r^4a_1`

This implies that

`(a_5)/(a_2)=r^3`

And so in this case we have

`(10)/(80)=r^3 \iff r^3 = (1)/(8) \iff r=(1)/(2)`