Question

Sum $\frac{1}{\sqrt{2}},-2,\frac{8}{\sqrt{2}},....$ to $7$ terms.

Answer 1

The sequence forms a G.P with

$a=\frac{1}{\sqrt{2}}$ and $r=-2\sqrt{2}$

$S_n=a\left(\frac{1-r^n}{1-r}\right)S_7=\frac{1}{\sqrt{2}}\left(\frac{1-{(-2\sqrt{2})}^7}{1-(-2\sqrt{2})}\right)S_7=\frac{1}{\sqrt{2}}\left(\frac{1+1056\sqrt{2}}{1+2\sqrt{2}}\right)S_7=\frac{1}{\sqrt{2}}\left(\frac{1+1056\sqrt{2}}{1+2\sqrt{2}}\right)S_7=\left(\frac{1+1056\sqrt{2}}{\sqrt{2}+4}\right)$