A geometric progression has first term 3 and common ratio 2
MATHEMATICS · Subjective · A Level · Mathematics · Sequences and series · Sequences and series
Problem
A geometric progression has first term 3 and common ratio 2.
(i) List explicitly the first five terms that lie in odd positions (that is, the 1st term, 3rd term, 5th term, and so on).
(ii) Deduce a general expression for the sum Sn(o) of the first n odd-positioned terms.
(iii) Hence calculate S5(o).
(iv) Comment on how the growth of Sn(o) compares with the growth of the ordinary sum of the first n terms of the same progression.