### Instruction: An infinite geometric series has common ratio $1/8$ and sum 60.  What is the first term of the series?### Response: So we know that the sum of a geometric series is equal to the first term divided by 1 minus the common ratio.
Right. So we can plug in what we know into that formula.
So the sum is 60, the common ratio is $1/8$ and the first term is $a$. So we have $60=a/(1-(1/8))$.
So we can multiply both sides by $1-(1/8)$ to get rid of the fraction.
That gives us $60(1-(1/8))=a$. So we can distribute the 60 on the left hand side to get $60-(60/8)=a$.
So $a=60-(7.5)$.