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Question
Find the nth terms of the sequences: 0.5, 0.55, 0.555, …
Solution
Let t1 = 0.5, t2 = 0.55, t3 = 0.555 and so on.
t1 = 0.5
t2 = 0.55 = 0.5 + 0.05
t3 = 0.555 = 0.5 + 0.05 + 0.005
∴ tn = 0.5 + 0.05 + 0.005 + ... upto n terms
But 0.5, 0.05, 0.005, … upto n terms are in
G.P. with a = 0.5 and r = 0.1
∴ tn = the sum of first n terms of the G.P.
∴ tn = `0.5{(1 - (0.1)^"n")/(1 - 0.1)}`
∴ tn = `0.5/0.9{1 - (0.1)^"n"}`
∴ tn = `5/9{1 - (0.1)^"n"}`
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