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प्रश्न
Find the sum of G.P. :
1 + 3 + 9 + 27 + .......... to 12 terms.
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उत्तर
Given G.P. : 1 + 3 + 9 + 27 + ..........
Here,
First term, a = 1
Common ratio, r =`3/1` = 3 ...(∵ r > 1)
Number of terms to be added, n = 12
∴ `S_n = (a(r^n - 1))/(r - 1)`
`=> S_12 = (1(3^12 - 1))/(3 - 1)`
= `(3^12 - 1)/2`
= `(531441 - 1)/2`
= `531440/2`
= 265720
संबंधित प्रश्न
Find, which of the following sequence from a G.P. :
`1/8, 1/24, 1/72, 1/216, ................`
The product of 3rd and 8th terms of a G.P. is 243. If its 4th term is 3, find its 7th term.
For the G.P. `1/27, 1/9, 1/3, ........., 81`; find the product of fourth term from the beginning and the fourth term from the end.
Q 2
Find the sum of G.P. :
`1 - 1/3 + 1/3^2 - 1/3^3 + .........` to n terms.
Find the sum of G.P. :
`sqrt(3) + 1/sqrt(3) + 1/(3sqrt(3)) + ..........` to n terms.
Find the sum of G.P. : 3, 6, 12, .........., 1536.
Find the geometric mean between `4/9` and `9/4`
Find the geometric mean between 14 and `7/32`
The first two terms of a G.P. are 125 and 25 respectively. Find the 5th and the 6th terms of the G.P.
