Question

1. The first term of a geometric progression is 1/2 and the fourth term is -4/27. Find the common ratio.

2. A geometric progression has a common ratio of 1/3 and the sum to infinity is 30. Find the first term of the progression.

Answer 1

1:- a1= 1/2 and a4 = a1r^3 = -4/27

therefore, a4=1/2(r^3)= -4/27

r=-2/3

2:-r=1/3 and S(infinite) =30=a/(1-r)

therefore, a= 30×(1-1/3) =20