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

 The required sum of first terms of the series is

Step-by-step explanation:  We are given to find the sum of the first five terms of a geometric series with first term and common ratio as follows :

We know that

the sum of first n terms of a geometric series with first term and common ratio r is given by

Therefore, the sum of first 5 terms of the given geometric series is given by

Thus, the required sum of first terms of the given geometric series is

hello from mrbilldoesmath!

answer:

a(n) - a(n-1) -3

discussion:

this ones a bit interesting. given a(n) = 5 - 3n consider this:

a(n-1) = 5 - 3(n-1)

          = (5 - 3n) + 3             => but a(n) = 5 - 3n, the first term

          = a(n)   + 3                 => subtract 3 from both sides

a(n-1) -3 = a(n)  

or

a(n) - a(n-1) -3

you,

mrb