# Answer to Question #4184 in Real Analysis for Junel

Question #4184

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).&

& 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).&

Expert's answer

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)

-1/2. So, (x sub n)=(1/2)*(-1/2)^(n-1)

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