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Question
Find the sum of the sequence `-1/3, 1, -3, 9, ..........` upto 8 terms.
Solution
Here, `1/(-1/3) = (-3)/1`
= `9/(-3)`
= –3
Thus, the given sequence is a G.P. with first term (a) = `-1/3` and common ratio (r) = –3 ...(∵ r < 1)
Number of terms to be added, n = 8
∴ `S_n = (a(1 - r^n))/(1 - r)`
`=> S_8 = (-1/3(1 - (-3)^8))/(1 + 3)`
= `(-1 + 3^8)/12`
= `1/12 (3^8 - 1)`
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