Question

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

Answer 1

`(1,562)/(125)`

Step-by-step explanation

the sum of a geometric serie is given by:

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

then

Step 1

a)Given

`\begin{gathered} a_1=10 \\ r=(1)/(5) \\ n=5\text{ \lparen first five terms\rparen} \end{gathered}`

b) now,replace in the formula

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

therefore, the answer is

`(1562)/(125)`

I hope this helps you