Question

9. Use the formula to evaluate the series 1 - 2 + 4 - 8+ ... -210-S,=a1(1 - 7")1-1In the formula for a finite series, a is the first term, r is the common ratio, and n is the number of terms.-10231023-341

Answer 1

Step 1: Write out the given data

`\begin{gathered} a_1=\text{ first term= 1} \\ r=\text{ common ration= }\frac{\sec ond\text{ term}}{\text{first term}} \\ \text{Second term= -2,} \\ r=(-2)/(1)=\text{ -2} \\ n=\text{ number of terms= 10.} \end{gathered}`

Step 2: Write out the formular and substitute the value to obtain the answer

`\begin{gathered} S_n=\text{ }(a_1(1-r^n))/(1-r) \\ S_(10)=\text{ }(1(1-(-2)^(10)))/(1-(-2)) \end{gathered}`
`\begin{gathered} S_(10)=\text{ }(1(1-1024))/(1+2) \\ S_(10)=\frac{\text{ 1(-1023)}}{3}=\text{ }\frac{\text{-1023}}{3}=\text{ -341} \end{gathered}`

The answer to series given is -341.