Question

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

Answer 1

I think you mean to say that the sequence is given recursively by


`\begin{cases}t_1=8\\t_n=-3t_(n-1)\end{cases}`

From this you can find a general pattern for the
`n`th term, but since we're only interested in determining
`t_5`, we can stop once we arrive at that. We have


`t_2=-3t_1`

`t_3=-3t_2=(-3)^2t_1`

`t_4=-3t_3=(-3)^3t_1`

`t_5=-3t_4=(-3)^4t_1`


`\implies t_5=8(-3)^4=8(81)=648`