Question

What is the sum of the first five terms of a geometric serieswith

Answer 1

$\frac{1,562}{125}$

Explanation

the sum of a geometric serie is given by:

$\begin{gathered} S_n=\frac{a(r^n-1)}{r-1} \\ \end{gathered}$

then

Step 1

a)Given

$\begin{gathered} a_1=10 \\ r=\frac{1}{5} \\ n=5\text{ \lparen first five terms\rparen} \end{gathered}$

b) now,replace in the formula

$\begin{gathered} S_{n}=\frac{a(r^{n}-1)}{r-1} \\ S_n=\frac{10((\frac{1}{5})^5-1)}{\frac{1}{5}-1} \\ S_n=\frac{10(\frac{1}{3125}-1)}{-\frac{4}{5}} \\ S_n=\frac{10(\frac{1-3125}{3125})}{-\frac{4}{5}} \\ S_n=\frac{10(\frac{-3124}{3125})}{-\frac{4}{5}}=\frac{-\frac{31240}{3125}}{-\frac{4}{5}}=\frac{156200}{12500}=\frac{1562}{125} \end{gathered}$

therefore, the answer is

$\frac{1562}{125}$

I hope this helps you