Let \(a_1,a_2,a_3,\dots\) be an arithmetic sequence. If \(\frac{a_4}{a_2} = 3\), what is \(\frac{a_5}{a_3}\)?
Let the sequence be
a, a+d, a+2d, a+3d, a+4d
\(\frac{a+3d}{a+d}=3 \qquad find \qquad \frac{a+4d}{a+2d}\\ 3a+3d=a+3d\\ 2a=0\\ a=0\\ so\\ \frac{a_5}{a_3}=\frac{a+4d}{a+2d}=\frac{4d}{2d}=2\)