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प्रश्न
Find the sum of the sequence `-1/3, 1, -3, 9, ..........` upto 8 terms.
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उत्तर
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)`
संबंधित प्रश्न
Find, which of the following sequence from a G.P. :
`1/8, 1/24, 1/72, 1/216, ................`
If the first and the third terms of a G.P. are 2 and 8 respectively, find its second term.
Find the seventh term from the end of the series :
`sqrt(2), 2, 2sqrt(2), ........., 32.`
If for a G.P., pth, qth and rth terms are a, b and c respectively; prove that : (q – r) log a + (r – p) log b + (p – q) log c = 0
Q 2
Find the sum of G.P. :
1 + 3 + 9 + 27 + .......... to 12 terms.
Find the sum of G.P. :
`1 - 1/2 + 1/4 - 1/8 + ..........` to 9 terms.
Q 3.1
Q 3.3
The first two terms of a G.P. are 125 and 25 respectively. Find the 5th and the 6th terms of the G.P.
