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Question
Find the sum of G.P. :
1 + 3 + 9 + 27 + .......... to 12 terms.
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Solution
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
RELATED QUESTIONS
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`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.
Q 1.2
If a, b and c are in A.P. and also in G.P., show that : a = b = c.
Find the sum of G.P. :
`1 - 1/3 + 1/3^2 - 1/3^3 + .........` to n terms.
Find the sum of G.P. : 3, 6, 12, .........., 1536.
Q 2
The first term of a G.P. is –3 and the square of the second term is equal to its 4th term. Find its 7th term.
The first two terms of a G.P. are 125 and 25 respectively. Find the 5th and the 6th terms of the G.P.
Find the sum of the sequence `-1/3, 1, -3, 9, ..........` upto 8 terms.
