Question

Write an explicit formula for each sequence.11. -64, -32, -16, -8,...

Answer 1

This is a geometric sequence with a common ration of half (1/2)

The general formula of a geometric sequence, with common ratio r, first term a

at the nth term, is given by

`\begin{gathered} U_n=ar^(n-1) \\ a=-64, \\ r=(-32)/(-64)=(1)/(2) \\ \text{Therefore} \\ U^{}_n=-64*((1)/(2))^(n-1)=-1*2^6*2^(-(n-1))^{}=-1*2^(-n+1+6)=(-1)2^(-n+7)_{} \\ \text{Therefore the explicit formula is} \\ U_n=(-1)2^(7-n) \end{gathered}`