Expert: Steve Holleran - 10/20/2007

Question
The first term of G.P is 4 and its fourth term is 0.5. calculate (A) the sixth term (B) the difference of the sum of the first four terms of the progression and its sum to infinity

Answer
Hi Ahmed,

Okay, so the progression has a1 = 4 and a4 = 1/2.

Since its geometric, the formula for the nth term is

            a(n) = a * r^n-1

so           a(4) = a * r^3

and then      1/2 = 4 * r^3   so r^3 = 1/8 and r = 1/2.

Then a(6) = 4 * (1/2)^5 = 4 * 1/32 = 1/8.

The sum of the first 4 terms is given by

           S(4) = [4(1 - (1/2)^4)] / (1 - 1/2)

                = [4(1 - 1/16)] / (1/2)

                = [4(15/16)] / (1/2)

                = (15/4) / (1/2) = 15/2 = 7.5

The sum to infinity is S(inf) = 4 / (1-1/2) = 8, so the difference is just 0.5.

Hope this helps.
Steve