Question

Find the sum of the sequence `-1/3, 1, -3, 9, ..........` upto 8 terms.

Answer 1

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)`