Question

For a G.P. a = 2, r = ${\displaystyle -\frac{2}{3}}$, find S₆

Answer 1

a = 2, r = ${\displaystyle -\frac{2}{3}}$

S_n = ${\displaystyle \frac{\text{a}(1-{\text{r}}^{\text{n}})}{1-\text{r}}}$, for r < 1

S₆ = ${\displaystyle \frac{2[1-{(-\frac{2}{3})}^6]}{1-(-\frac{2}{3})}}$

= ${\displaystyle \frac{2[1-{\left(\frac{2}{3}\right)}^6]}{\frac{5}{3}}}$

= ${\displaystyle \frac{6}{5}\left[\frac{729-64}{3^6}\right]}$

= ${\displaystyle \frac{6}{5}\left[\frac{665}{729}\right]}$

S₆ = ${\displaystyle \frac{266}{243}}$