Question

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

Answer 1

ANSWER:

2nd option: 78/25

STEP-BY-STEP EXPLANATION:

We have the following geometric series:

$a_n=\left(\frac{8}{25}\right)\cdot\left(\frac{5}{2}\right)^{\left(n-1\right)}$

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

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

The sum of the first 3 terms is 78/25