Question

Find the sum to indicated number of terms in each of the geometric progressions in $\sqrt{7},\sqrt{21},3\sqrt{7},.....$ n terms.

Answer 1

Here $a=\sqrt{7}andr=\frac{\sqrt{21}}{\sqrt{7}}=\sqrt{3}$

We konw that $S_n=\frac{a(r^n-1)}{r-1}$ when r > 1

$S_n=\frac{\sqrt{7\left[\right(\sqrt{3}{)}^n-1]}}{\sqrt{3}-1}$

= $\frac{\sqrt{7}}{\sqrt{3}-1}\times \frac{\sqrt{3}+1}{\sqrt{3}+1}\left[\right(3{)}^{\frac{n}{2}}-1]$

= $\frac{\sqrt{7}(\sqrt{3}+1)}{2}\left[\right(3{)}^{\frac{n}{2}}-1]$