Question

Th Write an recursive formula for an, the n term of the sequence 128, -32,8,... a1 an =

Answer 1

At first, we must find the common ratio between each two consecutive terms

`\begin{gathered} (-32)/(128)=-(1)/(4) \\ (8)/(-32)=-(1)/(4) \end{gathered}`

The common ratio is -1/4

The first term is 128

Then the recursive formula is

`a_1=1stterm;a_n=r.a_(n-1)`

r is the common ratio

r = -1/4

`a_1=128;a_n=(-(1)/(4)).a_(n-1)`