Question

Evaluate S5 for 600 + 300 + 150 + … and select the correct answer below. 1,162.5 581.25 37.5 18,600

Answer 1

`1,162.5`

1) The first step to solving this problem is to write the formula for this series.

Note that, we need to find the ratio so let's divide the 2nd term by the 1st term:

`(300)/(600)=(150)/(300)=(1)/(2)`

Since this is a Geometric series the ratio is the same.

2) Now, we can write the following expression to find the sum of the 5 terms:

`\begin{gathered} S_n=a_(1*)((1-q^n))/((1-q)) \\ \\ S=600((1-((1)/(2))^(600)))/((1-(1)/(2))) \\ \\ S=1,162.5 \end{gathered}`

3)So, the sum of the 5 first terms in this series is:

`1,162.5`