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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 fourth term, the seventh term and the last term of a geometric progression are 10, 80 and 2560 respectively. Find its first term, common ratio and number of terms.
Find the third term from the end of the G.P.
`2/27, 2/9, 2/3, .........,162.`
Q 6
Q 1.2
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. :
`sqrt(3) + 1/sqrt(3) + 1/(3sqrt(3)) + ..........` to n terms.
How many terms of the geometric progression 1 + 4 + 16 + 64 + …….. must be added to get sum equal to 5461?
Find the geometric mean between `4/9` and `9/4`
Q 7
