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If the sum of first n terms of a G.P. is...

If the sum of first n terms of a G.P. is S and the sum of its first 2n terms is 5S, then show that the sum of its first 3n terms is 21S.

Text Solution

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`S_n=(a(r^n-1))/(r-1)`
`S=(a(r^n-1))/(r-1)-(1)`
`S_(2n)=(a(r^(2n)-1))/(r-1)`
`5_s=(a(r^(2n)-1))/(r-1)-(2)`
Dividing equation 1 by 2
`1/5=(r^n-1)/(r^(2n)-1`
`r^(2n)-1=5r^n-5`
`r^(2n)-5r^n+4=0`
...
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