If in an AP,ratio of 4 t h term and 9 t h term is 1:3 ,find the ratio of 12th and 5th term?

Here's a slightly different (but no quicker) way:

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If in an AP,ratio of 4th term and 9th term is 1:3 ,find the ratio of 12th and 5th term?

\(\frac{a+3d}{a+8d}=\frac{1}{3}\\ 3a+9d=a+8d\\ d=-2a\\~\\ \mbox{Now find }\\ \frac{T_{12}}{T_5}\\ =\frac{a+11d}{a+4d}\\ =\frac{a-22a}{a-8a}\\ =\frac{-21a}{-7a}\\ =3\)

So the ratio is 3:1

Ther is probably a quicker way to do this.  ://