A geometric progression has first term a and common ratio r The 1st, 2nd and 4th terms of the geometric progression form the first three terms of an arithmetic progression a) Show that (r 1)(r r 1) 0 b) Given that the sum to infinity of the geometric progression is finite, find the exact value of r c) Find the sum to infinity of the geometric progression in terms of a

Question: A geometric progression has first term a and common ratio r. The 1st, 2nd and 4th terms of the geometric progression form the first three

A geometric progression has first term a and common ratio r. The 1st, 2nd and 4th terms of the geometric progression form the first three terms of an arithmetic progression.

a) Show that (r − 1)(r² + r − 1) = 0.

b) Given that the sum to infinity of the geometric progression is finite, find the exact value of r.

c) Find the sum to infinity of the geometric
progression in terms of a.

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