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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
Fourth and seventh terms of a G.P. are `1/18` and `-1/486` respectively. Find the G.P.
The product of 3rd and 8th terms of a G.P. is 243. If its 4th term is 3, find its 7th term.
Find the third term from the end of the G.P.
`2/27, 2/9, 2/3, .........,162.`
Q 6
If a, b and c are in A.P, a, x, b are in G.P. whereas b, y and c are also in G.P.
Show that : x2, b2, y2 are in A.P.
If a, b, c are in G.P. and a, x, b, y, c are in A.P., prove that `1/x + 1/y = 2/b`
Find the geometric mean between `4/9` and `9/4`
Q 2
Q 3.2
The sum of three numbers in G.P. is `39/10` and their product is 1. Find the numbers.
