Question

The sum of a geometric series with four terms is 60, and the common ratio is ???? = 1/2. Find the first term.

Answer 1

`a=32`

Explanation:

A geometric series is of the form
`a+ar+ar^2+ar^3+...`, 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:

`a+ar+ar^2+ar^3=a+a(1)/(2)+a(1)/(4)+a(1)/(8)=60`

Which we can keep calculating as
`a(1+(1)/(2)+(1)/(4)+(1)/(8))=a((8+4+2+1)/(8))=a((15)/(8))=60`

So we can solve for a:

`a=((8)(60))/(15)=32`