A geometric progression has first term a where a‡0 and common ratio r where r‡1. the difference between the fourth and first term is equal to four times the difference between the third term and the second term.
i) show that r³ - 4r² + 4r -1 = 0
ii) find two possible values for the ratio of the geometric progression.
ii) for the value of r which the progression is convergent, prove that the sum to infinity is 1/2 a (1 + √5)