Question

In a geometric sequence, if a3 = ‒5 and a6 = 40, determine a1, r, and an. Then write the first three terms of the sequence.

Answer 1

`a_4=ra_3`

`a_5=ra_4=r^2a_3`

`a_6=ra_5=r^3a_3`


`40=-5r^3\implies r^3=-8\implies r=-2`


`a_3=ra_2=r^2a_1`


`-5=(-2)^2a_1\implies a_1=-\frac54`

You know the first and third terms,
`a_1` and
`a_3`, so you just need to find the second term
`a_2`:


`a_2=ra_1\implies a_2=-2\left(-\frac54\right)=\frac52`