Answer:
[tex]-1.75[/tex]
Step-by-step explanation:
It can help to write some or all of the terms of the series. This can help you identify the first term as -7/3 and the common ratio as -1/3. Then the formula for the sum of a geometric series can be used to find the sum of 6 terms.
[tex]=7\left(\dfrac{-1}{3}\right)^1+7\left(\dfrac{-1}{3}\right)^2+7\left(\dfrac{-1}{3}\right)^3+7\left(\dfrac{-1}{3}\right)^4+7\left(\dfrac{-1}{3}\right)^5+7\left(\dfrac{-1}{3}\right)^6\\\\S_6=a_1\cdot\dfrac{r^6-1}{r-1} \quad\text{for $a_1=-7/3$ and r=-1/3}\\\\S_6=\left(\dfrac{-7}{3}\right)\left(\dfrac{\left(\dfrac{-1}{3}\right)^6-1}{\dfrac{-1}{3}-1}\right)=\left(\dfrac{-7}{3}\right)\left(\dfrac{\dfrac{-728}{729}}{\dfrac{-4}{3}}\right)=\dfrac{(-7)(728)(3)}{(3)(729)(4)}[/tex]
[tex]S_6=\dfrac{(-7)(182)}{729}=-\dfrac{1274}{729}\approx -1.75[/tex]
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Or, you can simply add up the terms on your calculator.
-2.33333 +0.777778 -0.259259 +0.0864198 -0.0288066 +0.00960219
The first two or three terms will get you a sum close enough to choose the correct answer.
