Question

-5, -2, -4/5, -8/25,… find the sum

Answer 1

Explanation:

We determine if it is geometric progression or arithmetic

Geometric progression:

$r\text{ = common ratio = }\frac{next\text{ term}}{\text{previous term}}$$\begin{gathered} r\text{ = }\frac{-2}{-5}=\frac{2}{5} \\ r\text{ = }\frac{-4}{5}\div-2\text{ = }\frac{-4}{5}\times\frac{1}{-2} \\ r\text{ = }\frac{2}{5} \end{gathered}$

The common ratio is the same. so we would apply sum of geometric progression:

$S_n=\frac{a(1-r^n)}{1-r}$$\begin{gathered} a\text{ = -5} \\ r\text{ = 2/5} \\ T\text{here are 4 terms, n = 4} \\ S_4=\frac{-5(1-(\frac{2}{5})^4)}{1-\frac{2}{5}} \end{gathered}$$undefined$