Find the sum to indicated number of terms in each of the geometric progressions : `sqrt(7),sqrt(21),7 3,`. . . n terms.

Answer

N/a

Explanation

`"Given G.P : "sqrt(7),sqrt(21),3sqrt(7),...`
`"First term "a_(1)=a=sqrt(7)`
`"Second term "a_(2)=sqrt(21)`
`therefore" Common ratio r"=(a_(2))/(a)=(sqrt(21))/(sqrt(7))=sqrt(3)`
`because" Sum of n terms of G.P."S_(n)=(a(r^(n)-1))/(r-1)`
`=(sqrt(7)[(sqrt(3))^(n)-1])/((sqrt(3)-1))=(sqrt(7)(sqrt(3)+1)[(sqrt(3))^(n)-1])/((sqrt(3)-1)(sqrt(3)+1))`
`=(sqrt(7)(sqrt3+1))/(2)cdot[(3)^(n//2)-1]`
`therefore" Sum of n terms "S_(n)=(sqrt(7)(sqrt3+1))/(2)cdot[(3)^(n/2)-1]`