How do you find the sum of the geometric series $2-10+50-...$ to 6 terms?

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Answer 1 · 2016-11-25T22:30:14

$S_n=-5208$

Find the sum of the geometric sequence $2, -10, 50...$ to 6 terms.

A geometric sequence is formed by multiplying a term by a number called the common ratio $r$ to get the next term.

The formula for a sum of a geometric sequence is

$S_n=frac(a_1(1-r^n))(1-r)$
where $a_1$ is the first term, $r$ is the common ratio, and $n$ is the number of the term,

In this example, $r$ is found by dividing a term by the previous term.

$r=(-10)/2 =-5color(white)(aaa)$ $n=6color(white)(aaa)$ and $a_1=2$

$S_n= frac(2*(1-(-5)^6))(1- -5)= frac(2*(1-15625))(6)=frac(2*-15624)(6)$

$S_n=-5208$

Alternatively, you could continue the sequence to 6 terms and add them.

First find the next 3 terms by multiplying the previous term by $r=-5$

$2, -10,50, -250, 1250, -6250$

Then add these 6 terms together. The sum is $=5208$

How do you find the sum of the geometric series 2-10+50-...2-10+50-... to 6 terms?