Answer:
[tex]a=32[/tex]
Step-by-step explanation:
A geometric series is of the form [tex]a+ar+ar^2+ar^3+...[/tex], where r is the common ratio, and a is the first term of the series. This means that for our case, where the r is 1/2 and the first 4 terms add up to 60, we have:
[tex]a+ar+ar^2+ar^3=a+a\frac{1}{2}+a\frac{1}{4}+a\frac{1}{8}=60[/tex]
Which we can keep calculating as [tex]a(1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8})=a(\frac{8+4+2+1}{8})=a(\frac{15}{8})=60[/tex]
So we can solve for a:
[tex]a=\frac{(8)(60)}{15}=32[/tex]
