Question

Find S7 of the sum of the geometric series. a1 = 729, a? = 1, r = 1

Answer 1

Let's write out the formula for the sum of geometric series,

`S_n=(a(1-r^n))/(1-r)`
`\begin{gathered} \text{where a=first term=729} \\ r=\text{common ratio=}(1)/(-3) \\ S_7=?,\text{ where n= number of terms=7} \end{gathered}`

Let's solve for the sum of seven geometric series,

`\begin{gathered} S_7=(729(1-(-(1)/(3))^7))/(1-(-(1)/(3))) \\ =(729(1-(-(1)/(2187))))/(1+(1)/(3)) \\ =(729(1+(1)/(2187)))/((4)/(3)) \end{gathered}`

`\begin{gathered} S_7=(729(1(1)/(2187)))/((4)/(3)) \\ =(729((2188)/(2187)))/((4)/(3))=((2188)/(3))/((4)/(3)) \\ =(2188)/(3)\frac{\text{.}}{.}(4)/(3) \\ =(2188)/(3)*(3)/(4)=547 \end{gathered}`

Hence,

`S_7=547`

Therefore, option 5 is the correct answer.

Option 5 is none of these are correct.