Question

Find the 4th term if the sequend in which a1 = 2 and a n+1 = -4a n + 2

***PLEASE HELP**

Answer 1

Given that

`a_(n+1)=-4a_(n+2)` and
`a_1=2`

For n = 0,

`a_1=-4a_2 \\ \\ 2=-4a_2 \\ \\ \Rightarrow a_2=-(1)/(2)`

common ratio =
`(a_2)/(a_1)=(-(1)/(2))/(2)=-(1)/(4)`

4th term =
`a_4=a_1r^(4-1)=2(-(1)/(4))^3=2(-(1)/(64))=-(1)/(32)`