Answer to Question #4184 in Real Analysis for Junel

Question

The first five terms of a sequence (x sub n) are given below.&
& 1/2,-1/4,1/8,-1/16,.....

assuming that the "natural pattern" indicated by these terms persist, give a formula for the nth term (x sub n).&

Answer 1

it's obvois that this is geometric progression with (x sub 1) = 1/2 and q =
-1/2. So, (x sub n)=(1/2)*(-1/2)^(n-1)