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InterviewSolution
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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. |
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Answer» `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` Let`r^n=t` `t^2-5t+4=0` `(t-1)(t-4)=0` `t=1,4` `r^n=4` `S=(a(r^n-1))/(r-1)` `r-1=(a(r^n-1))/S-(3)` `S_(3n)=(a(r^(3n)-1))/(r-1)` `S_(3n)=(a(r^n)^3-1*5)/(a(r^n-1)` `S_(3n)=((4^3-1)*5)/(4-1)` `S_(3n)=215`. |
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