Question

What is the 8th partial sum of 1,600 – 400 + 100 – 25 + …? Round your answer to the thousandths place.

Answer 1

Given the series 1,600 – 400 + 100 – 25 + …

The series is a geometric series because it has a common ratio

The common ratio is

`\begin{gathered} r=(-400)/(1600) \\ r=(-1)/(4) \end{gathered}`
`\begin{gathered} \text{ For a geometric series, the sun of nth term is given by the formula} \\ s_n=(a(1-r^n))/(1-r) \\ Where\text{ a = first term = 1600} \\ r=\text{common ratio = -1/4 = -0.25} \\ n=\text{ number of terms} \\ \text{For this question, n=8} \end{gathered}`
`\begin{gathered} s_8=(1600(1-(-0.25)^8))/(1-(-0.25))_{}_{} \\ s_8=(1600(1-0.0000152587))/(1.25)=(1600(0.9999847))/(1.25) \\ s_8=(1599.97558)/(1.25) \\ \\ s_8=1279.9804 \end{gathered}`

To the nearest thousandth, we have 1,279.980

Hence, The 8th partial sum of the series is 1,279.980 to the nearest thousandth