Question

If a1 = 4 and an = -3an-1 then find the value of a4.

Answer 1

`a_4 = -108`

Explanation:

Given

`a_n = -3a_(n-1)`

`a_1 = 4`

Required

Find
`a_4`

`a_4 = -3a_(4-1)`

`a_4 = -3a_3`

We calculate for a3

`a_3 = -3a_(3-1)`

`a_3 = -3a_2`

Calculate for a2

`a_2 = -3a_{2-1`

`a_2 = -3a_1`

Substitute 4 for a1

`a_2 = -3*4`

`a_2 = -12`

Substitute -12 for a2 in
`a_3 = -3a_2`

`a_3 = -3 * -12`

`a_3 = 36`

Substitute 36 for a3 in
`a_4 = -3a_3`

`a_4 = -3*36`

`a_4 = -108`