Essentially this is asking you to sum the first three values of the geometric series that starts with i being 1 and has the rule of ([tex]8(\frac{1}{4})^{i-1}[/tex]).
Since we must sum the first three geometric values we need to see what the value of i will be for the first three. The sigma notation shows us that the first i will be equal to 1. This means the second i is 2 and the third i is 3.
Knowing this you can plug in the corresponding i values into ([tex]8(\frac{1}{4})^{i-1}[/tex]) and sum it all together
([tex]8(\frac{1}{4})^{1-1}[/tex]) + ([tex]8(\frac{1}{4})^{2-1}[/tex]) + ([tex]8(\frac{1}{4})^{3-1}[/tex])
([tex]8(\frac{1}{4})^{0}[/tex]) + ([tex]8(\frac{1}{4})^{1}[/tex]) + ([tex]8(\frac{1}{4})^{2}[/tex])
([tex]8(1)[/tex]) + ([tex]8(\frac{1}{4})[/tex]) + ([tex]8(\frac{1}{16})[/tex])
(8) + (2) + ([tex]\frac{1}{2})[/tex])
10 + [tex]\frac{1}{2})[/tex]
[tex]\frac{21}{2})[/tex]
10.5
Hope this helped!
~Just a girl in love with Shawn Mendes
