Question

What is the sum of the first five terms of a geometric series with a1=6 and r=1/3

Answer 1

The sum of n terms of a geometric series is found using the following formula:

`S _(n) = (a(1-r^(n)))/(1-r)`
where a is the first term and r is the common ratio.
In your question, a = 6 and r = 1/3, so we have:

`S_(5) =(6(1-((1)/(3))^5))/(1-(1)/(3))`
which simplifies to:
`S_(5)=(6(1-(1)/(243)))/((2)/(3))`

Answer 2

242/27 is the answer as an improper fraction

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