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Question
The 4th and the 7th terms of a G.P. are `1/27` and `1/729` respectively. Find the sum of n terms of this G.P.
Solution
For a G.P.,
4th term = ar3 = `1/27`
7th term = ar6 = `1/729`
Now, `(ar^6)/(ar^3) = (1/729)/(1/27)`
`=> r^3 = 1/27 = (1/3)^3`
`=> r = 1/3` ...(∵ r < 1)
`=> a xx 1/27 = 1/27`
`=>` a = 1
`S_n = (a(1 - r^n))/(1 - r)`
`=> S_n = (1(1 - (1/3)^n))/(1 - 1/3)`
= `(1 - 1/3^n)/(2/3)`
= `3/2(1 - 1/3^n)`
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