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Find the nth terms of the sequences: 0.5, 0.55, 0.555, … - Mathematics and Statistics

Sum

Find the nth terms of the sequences: 0.5, 0.55, 0.555, …

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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"}`

Concept: Sum of the First n Terms of a G.P.
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APPEARS IN

Balbharati Mathematics and Statistics 1 (Commerce) 11th Standard Maharashtra State Board
Chapter 4 Sequences and Series
Exercise 4.2 | Q 7. (i) | Page 55
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