The sum of the first n terms in the infinite geometric sequence {1/4, 1/8, 1/16, ...} is 255/512. Find n.

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AnonymousConfusedGuy Jan 16, 2018

#1**+1 **

The common ratio, r, can be determined as the ratio of the terms

a_{n+1} / a_{n } so we have.... (1/8) / (1/4) = 4/8 = 1/2

And we have that

255/512 = 1/4 [ 1 - (1/2)^n ] / [ 1 - 1/2 ]

255/512 = 1/4 [ 1 - (1/2)^n ] / (1/2)

255/512 = (1/2) [ 1 - (1/2)^n ] multiply both sdes by 2

255* 2 / 512 = 1 - (1/2)^n rearrange as

(1/2)^n = 1 - 510/512

(1/2)^n = [ 512 - 510 ] / 512 = 2 / 512 = 1/256

Take the log of both sides

log (1/2)^n = log (1/256) and we can write

n = log (1/256) / log (1/2)

n = 8 â‡’ 8 terms

CPhill Jan 16, 2018