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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
Which term of the G.P.:
`-10, 5/sqrt(3), -5/6,....` is `-5/72`?
The fifth term of a G.P. is 81 and its second term is 24. Find the geometric progression.
Find the geometric progression with 4th term = 54 and 7th term = 1458.
Q 6
If each term of a G.P. is raised to the power x, show that the resulting sequence is also a G.P.
Find the sum of G.P. :
`(x + y)/(x - y) + 1 + (x - y)/(x + y) + ..........` upto n terms.
How many terms of the geometric progression 1 + 4 + 16 + 64 + …….. must be added to get sum equal to 5461?
Q 3.3
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.
Find a G.P. for which the sum of first two terms is – 4 and the fifth term is 4 times the third term.
