Problem:
A geometric sequence (an) has a1=sinx,a2=cosx, and a3=tanx for some real number x. For what value of n does an=1+cosx ?
Answer Choices:
A. 4
B. 5
C. 6
D. 7
E. 8 Solution:
The ratio between consecutive terms of the sequence is
r=a1a2=cotx
so a4=(tanx)(cotx)=1, and r is also equal to
a2a4=cosx1
Therefore x satisfies the equation cos3x=sin2x=1−cos2x, which can be written as (cos2x)(1+cosx)=1. The given conditions imply that cosx=0, so this equation is equivalent to