Question

Which expression defines Sn for an = 5(1/3)^n?

Answer 1

If the first term is 5/3 and the common difference is 1/3. Then the infinite sum of the geometric series will be 2.5.

What is a series?

The sum of sequence terms is a series. That is, it is a list of integers connected by addition operations.

The sequence is given in the form of a variable.

$\rm a_n = 5 \left (\dfrac{1}{3} \right)^{n}$

The first term will be

$\rm a_1 =\dfrac{5}{3}$

And the common ratio will be

$\rm r =\dfrac{1}{3}$

Then the sum of the geometric series will be given as

$\rm S_{\infty} = \dfrac{a_1}{1-r}\\\\\\S_{\infty} = \dfrac{5/3}{1-1/3}\\\\\\S_{\infty} = \dfrac{5/3}{2/3}\\\\\\S_{\infty} = \dfrac{5}{2}\\\\\\S_{\infty} = 2.5$

More about the series link is given below.

brainly.com/question/10813422

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