# Geometric progression

Find the number of terms in G.Pgiven thatits first&last term are 5 1/3k&243k/256 respectively&that its common ratiois3/4

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1. first term = a = 5 1/3k or (16/3)k
r = 3/4

last term = ar^(n-1) = 243k/256 = (243/256)k

(16/3)k (3/4)^(n-1) = (243/256)k
(3/4)^(n-1) = (243/256)(3/16) = 729/4096 = 3^6 / 4^6

(3/4)^(n-1) = (3/4)^6
n-1 = 6
n = 7

you have 7 terms

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