Question

How do you find the first term of a geometric sequence whose fourth term is -6 and whose common ratio is 1/3?

Answer 1

The first term is `(-162)`

Explanation:

Suppose the first term is `a_1`
then (since the common ratio is `1/3`)

`color(white)("XXX")a_2= (1/3)xxa_1`

`color(white)("XXX")a_3= (1/3)xxa_2 = (1/3)^2xxa_1`

`color(white)("XXX")a_4= (1/3)xxa_3 = (1/3)^3xxa_1`

We are told
`color(white)("XXX")a_4 = -6`

So
`color(white)("XXX")(1/3)^3xxa_1=-6`

`color(white)("XXX")1/27xxa_1 =-6`

`color(white)("XXX")a_1=(-6)xx27 = -162`