Question

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

Answer 1

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}`