Question

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

Answer 1

The sum of the first three terms of the geometric series is 128700.

Step-by-step explanation:

To find the sum of the first three terms of the geometric series represented by the formula an = (825)(52)(n - 1), we need to substitute the values of n into the formula and evaluate.

First, we substitute n = 1 into the formula:

a₁ = (825)(52)(1 - 1) = 0

Next, we substitute n = 2 into the formula:

a₂ = (825)(52)(2 - 1) = 42900

Finally, we substitute n = 3 into the formula:

a₃ = (825)(52)(3 - 1) = 85800

To find the sum, we add the three terms together:

Sum = a₁ + a₂ + a₃ = 0 + 42900 + 85800 = 128700

Answer 2

2nd option: 78/25

STEP-BY-STEP EXPLANATION:

We have the following geometric series:

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

The sum of the first 3 terms is 78/25