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Questions
The first term of a G.P. is 27 and its 8th term is `1/81`. Find the sum of its first 10 terms.
The first term of a G.P. in 27. If the 8th term be `1/81`, what will be the sum of 10 terms?
Solution
Given,
First term, a = 27
8th term = ar7 = `1/81`
n = 10
Now,
`(ar^7)/a = (1/81)/27`
`=> r^7 = 1/2187`
`=> r^7 = (1/3)^7`
`=> r = 1/3` ...(∵ r < 1)
∴ `S_n = (a(1 - r^n))/(1 - r)`
`=> S_10 = (27(1 - (1/3)^10))/(1 - 1/3)`
= `(27(1 - 1/3^10))/(2/3)`
= `(27 xx 3)/2(1 - 1/3^10)`
= `81/2 (1 - 1/3^10)`
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