If 6 times the sixth term of an arithmetic progression is equal to 9 times the 9th term, find

Question

the 15th term.

Answer 1

6(a+5d)=9(a+8d)
6a+30d=9a+72d
3a = -42d
a = -14d

So, there are lots of answers. For example, if d=1, a=-14 and the sequence is
-14,-13-,12,-11,-10,-9,-8,-7,-6, ...
6(-9)=9(-6)