The sum of the first n terms in the infinite geometric sequence {14,18,116,…} is 255512 . Find n.
We have that
255/512 = (1/4) [ 1 - (1/2)^n ] / [ 1 - 1/2] simplify
255/512 = (1/2) [ 1 - (1/2)^n ]
255 / 256 = 1 - (1/2)^n
(1/2)^n = 1 - 255/256
(1/2)^n = 1/256
(1/2)^n = (1/2)^8
So....n = 8
+847 
