**??? - 2013 JUNE Q6**

6.

i) Another geometric progression has first term 2

*S*is the sum to infinity of a geometric progression with first term*a*and common ratio*r*.i) Another geometric progression has first term 2

*a*and common ratio*r.*Express the sum to infinity of this progression in terms of*S*. [1]

(ii) A third geometric progression has first term

*a*and common ratio*r*^{2}. Express, in its simplest form, the sum to infinity of this progression in terms of*S*and*r*. [2]