How many terms are there in a geometric series if the first term is 3, the common ratio is 4, and the sum of the series is 1,023?

Hint: cap s sub n equals start fraction a sub one left parenthesis one minus r to the power of n end power right parenthesis over one minus r end fraction comma r ≠ 1, where a1 is the first term and r is the common ratio.

Question

How many terms are there in a geometric series if the first term is 3, the common ratio is 4, and the sum of the series is 1,023?

Hint: cap s sub n equals start fraction a sub one left parenthesis one minus r to the power of n end power right parenthesis over one minus r end fraction comma r ≠ 1, where a1 is the first term and r is the common ratio.

mathmale · Answer

I don't see the point in your spelling out the formula.  Why not write the formula symbolically?

Represent the first term by a.  Here, its value is 3.
Represent the common ratio by r.  What is the value of r?
Represent the sum of the series by S.  What is S?