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Find the sum of the first three terms of the geometric series represented by the formula an = (825)(52)(n - 1).

Find The Sum Of The First Three Terms Of The Geometric Series Represented By The Formula An 82552n 1 class=

Sagot :

ANSWER:

2nd option: 78/25

STEP-BY-STEP EXPLANATION:

We have the following geometric series:

[tex]a_n=\left(\frac{8}{25}\right)\cdot\left(\frac{5}{2}\right)^{\left(n-1\right)}[/tex]

We calculate the sum, replace n by 1,2,3, just like this:

[tex]\begin{gathered} s_n=\left(\frac{8}{25}\right)\cdot\left(\frac{5}{2}\right)^{\left(1-1\right)}+\left(\frac{8}{25}\right)\cdot\left(\frac{5}{2}\right)^{\left(2-1\right)}+\left(\frac{8}{25}\right)\cdot\left(\frac{5}{2}\right)^{\left(3-1\right)} \\ s_n=\left(\frac{8}{25}\right)\cdot\left(\frac{5}{2}\right)^0+\left(\frac{8}{25}\right)\cdot\left(\frac{5}{2}\right)^1+\left(\frac{8}{25}\right)\cdot\left(\frac{5}{2}\right)^2 \\ s_n=\frac{8}{25}+\frac{4}{5}+\frac{8}{4} \\ s_n=\frac{32+80+200}{100} \\ s_n=\frac{312}{100} \\ s_n=\frac{78}{25} \end{gathered}[/tex]

The sum of the first 3 terms is 78/25

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