Question

Find the sum of the first 6 terms of the following sequence. Round to the nearesthundredth if necessary.

Answer 1

The sequence given is,

`8,4,2,\ldots`

Let us look for the common ration (r)

`\begin{gathered} r=\frac{\text{second term}}{\text{first term}}=(4)/(8)=(1)/(2) \\ \therefore r=(1)/(2) \end{gathered}`

Given that

`a=first\text{ term=8}`

The formula for the sum of sum of a finite geometric series is

`S_n=(a_1-a_(1r^n))/(1-r)`

We are to look for sum of first 6 terms

`n=6`

Hence,

`\begin{gathered} S_6=(8-8*((1)/(2))^6)/(1-(1)/(2))=(8-8*(1)/(64))/((1)/(2))=(8-(1)/(8))/((1)/(2)) \\ S_6=(7(7)/(8))/((1)/(2))=(63)/(8)/(1)/(2)=(63)/(8)*(2)/(1)=(126)/(8)=15.75 \end{gathered}`

Therefore, the sum of 6 first term is 15.75.