Geometric Series

Question

1. In a geometric series, t1=3 and S3=21. Determine the common ratio and an expression for the sum of the first k terms.

Answer 1

3 + 3r + 3r² = 21

1 + r + r² = 7

     r + r² = 6  & the solution to this quadratic equation is r = 2 (which you can guess at without any other steps).

 

Now that you know the initial term a = 3 and r = 2, use the general formula for the sum of k terms (perhaps learned as the sum of n terms).