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

User DMisener
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1 Answer

2 votes

Answer:


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

User Hemant Gangwar
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