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प्रश्न
Find the nth terms of the sequences: 0.2, 0.22, 0.222, …
उत्तर
Let t1 = 0.2, t2 = 0.22, t3 = 0.222 and so on.
t1 = 0.2
t2 = 0.22 = 0.2 + 0.02
t3 = 0.222 = 0.2 + 0.02 + 0.002
∴ tn = 0.2 + 0.02 + 0.002 + ... upto n terms
But 0.2, 0.02, 0.002, … upto n terms are in
G.P. with a = 0.2 and r = 0.1
∴ tn = the sum of first n terms of the G.P.
∴ tn = `0.2{(1 - (0.1)^"n")/(1 - 0.1)}`
∴ tn = `0.2/0.9{1 - (0.1)^"n"}`
∴ tn = `2/9{1 - (0.1)^"n"}`
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