Question

Find S3 of the sum of the geometric series. az = 4, a3 = 1, r= 1

Answer 1

Given:

a1 = 4

a3 = 1

r = ½

Let's find the S3 of the sum of the geometric series.

Apply the sum of geometric series formula below:

`S_n=(a_1(1-r^n))/(1-r)`

Let's solve for S3.

Substitute the values into the equation.

Where: n = 3

Thus, we have:

`S_3=\frac{4(1-((1)/(2))^3)^{}^{}}{1-(1)/(2)}`

Solving further:

`\begin{gathered} S_3=(4(1-((1)/(2)\cdot(1)/(2)\cdot(1)/(2))))/((1)/(2)) \\ \\ S_3=(4(1-(1)/(8)))/((1)/(2)) \\ \\ S_3=(4((7)/(8)))/((1)/(2)) \\ \\ S_3=(4\ast(7)/(8))/((1)/(2)) \\ \\ S_3=((7)/(2))/((1)/(2)) \\ \\ S_3=(7)/(2)\ast(2)/(1) \\ \\ S_3=7 \end{gathered}`

Therefore, the S3 of the sum of the given geometric series is 7

ANSWER:

7