Question

Find S3 of the sum of the geometric series. ai = 4, a3 = 1, r= 1 7 2

Answer 1

7 (option A)

Step-by-step explanation:
`\begin{gathered} a_1\text{ = 4} \\ a_3\text{ = 1} \\ r\text{ = 1/2} \\ r\text{ is less than 1 here} \end{gathered}`
`\begin{gathered} \text{Sum of geometric series:} \\ s_n\text{ = }\frac{a(1-r^n)}{1-r^{}} \\ for\text{ }when\text{ r is less than 1} \end{gathered}`
`\begin{gathered} \text{nth term of a geometric seqeunce:} \\ a_n=a_1r^{\mleft\{n-1\mright\}} \\ n\text{ =3} \\ a_3\text{ = }4((1)/(2))^(3-1) \\ a_3\text{ = }4((1)/(2))^2 \\ a_3\text{ = }4((1)/(4)) \\ a_3\text{ = }1 \end{gathered}`
`\begin{gathered} s_3=\text{ }\frac{4(1-((1)/(2))^3_{})}{1-((1)/(2))} \\ s_3=\text{ }\frac{4(1-((1)/(8))}{1-((1)/(2))^{}} \end{gathered}`
`\begin{gathered} s_3=\text{ }(4((8-1)/(8)))/((2-1)/(2))\text{ = }(4((7)/(8)))/((1)/(2)) \\ s_3=((7)/(2))/((1)/(2))\text{ = }(7)/(2)/(1)/(2) \\ s_3=\text{ }(7)/(2)*(2)/(1) \\ s_3=\text{ 7 (option A)} \end{gathered}`