Question

Determine whether the sequence converges or diverges. If it converges, give the limit.

108, -54, 27,-(27/2) , ...

(a) Converges; 216

(b) Diverges

(c) Converges; 540

(d) Converges; 0

Answer 1

(d) Converges; 0

The answer is d because a geometric sequence converges only if the absolute value of the common ratio (r) is less than one. It diverges if the ratio (r) is greater than or equal to 1. This sequence converges because r= - 1/2 or -0.5, which is less than 1. And the limit seems to approach zero, since the values keep getting smaller.