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Evaluate each geometric series described. 2 - 6 + 18 – 54.... n=17

User Xavc
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1 Answer

15 votes
15 votes

The formula for the sum of a geometric series is given as:


S_n=a_1((1-r^n)/(1-r))

Note that r is the common ratio, a1 is the first term.

To find the common ratio, find the ratio of any two consecutive terms, say a1 and a2:


\begin{gathered} r=(a_2)/(a_1) \\ r=(-6)/(2) \\ r=-3 \end{gathered}

Next, substitute the values n=17, r=-3, and a1=2 into the formula:


S_(17)=2((1-(-3)^(17)))/(1-(-3)))

Use a calculator to evaluate the expression for the sum:


\begin{gathered} S_(17)=2((1-(-129140163))/(4)) \\ =2((1+129140163)/(4)) \\ =2((129140164)/(4)) \\ =64570082 \end{gathered}

User Bjorkblom
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