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

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

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

$\begin{gathered} S_n=\text{ }\frac{a_1(1-r^n)}{1-r} \\ S_{10}=\text{ }\frac{1(1-(-2)^{10})}{1-(-2)} \end{gathered}$$\begin{gathered} S_{10}=\text{ }\frac{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.