Let denote the sum of the first terms of an arithmetic progression and denote that of…

MATHEMATICS · Single correct · A Level · Mathematics · Sequences and series · Sequences and series

Problem

Let

S_n^{(A)}

denote the sum of the first

n

terms of an arithmetic progression and

S_n^{(G)}

denote that of a geometric progression. Both progressions have first term

5

. The arithmetic progression has common difference

5

, while the geometric progression has common ratio

r

where

0<r<1

. Which statement describes the behaviour of

S_n^{(A)}

and

S_n^{(G)}

n

becomes very large? (a) Both

S_n^{(A)}

and

S_n^{(G)}

approach finite limits. (b)

S_n^{(A)}

grows without bound, but

S_n^{(G)}

approaches a finite limit. (c) Both

S_n^{(A)}

and

S_n^{(G)}

grow without bound. (d)

S_n^{(A)}

approaches a finite limit, but

S_n^{(G)}

grows without bound.