Question

What is the sum of the first five terms of a geometric series with a1 =20 and r =1/4?

Answer 1

The sum of the first n terms in a geometric sequence given the first term (a1) and the common ratio (r) is calculated through the equation,

                            Sn = (a1(1−r^n) / (1−r)

Substituting the known terms,
                           Sn = (20)(1 - (1/4)^4)) / (1 - 1/4)
                           Sn = 26.5625

Thus, the sum of the first four terms is 26.5625.