Question

Find the common ratio.

5
Σ6(2)n-1
n = 1
S = 6(1-[?]
1 - [?]
r = [ ? ]
Remember: for a geometric series, S = a(¹1 – r")
1-r

Answer 1

r = 2

Explanation:

You want the common ratio for the given geometric series.

Ratio

In the expression for the general term of a geometric series, the ratio is the base of the exponential factor.

an = a·(r)^(n-1)

Compare to ...

an = 6(2)^(n-1)

and you see that the common ratio is ...

r = 2

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Additional comment

The value of the common ratio, 2, goes in all of the green boxes in the figure. The value of the sum is 186.

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