Question

-5, -2, -4/5, -8/25,… find the sum

Answer 1

Step-by-step 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{ = }(-2)/(-5)=(2)/(5) \\ r\text{ = }(-4)/(5)/-2\text{ = }(-4)/(5)*(1)/(-2) \\ r\text{ = }(2)/(5) \end{gathered}`

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

`S_n=(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=(-5(1-((2)/(5))^4))/(1-(2)/(5)) \end{gathered}`