For a geometric progression with positive first term and common ratio
MATHEMATICS · Single correct · A Level · Mathematics · Sequences and series · Sequences and series
Problem
For a geometric progression with positive first term 5 and common ratio r>0, let Sn denote the sum of the first n terms. Which statement is always true?
(a) If 0<r<1, then Sn decreases as n increases.
(b) If r=1, then Sn is constant and equal to 5.
(c) If r>1, then Sn grows without bound as n increases.
(d) If r>1, then Sn converges to r−15.