Question

Find the 5th term of the sequence in which t1 = 8 and tn = -3tn-1.

Answer 1

One way to do it is to find an explicit formula for the
`n`th term.


`t_n=-3t_(n-1)=-3(-3t_(n-2))=(-3)^2t_(n-2)=(-3)^2(-3t_(n-3))=(-3)^3t_(n-3)=\cdots`

The pattern suggests that the
`n`th term is given by
`t_n=(-3)^(n-1)t_1`, and so the fifth term is
`t_5=(-3)^4t_1=648`.

Another way to do it would be to plug
`t_1` into the recursive formula to find
`t_2`, then
`t_3`, and so on.


`t_2=-3t_1=-24`

`t_3=-3t_2=72`

`t_4=-3t_3=-216`

`t_5=-3t_4=648`