a₁ = 3

 $\frac{{\mathrm{S}}_{\mathrm{m}}}{{\mathrm{S}}_{\mathrm{n}}}=\frac{{\mathrm{S}}_{5\mathrm{n}}}{{\mathrm{S}}_{\mathrm{n}}}=\frac{\frac{5\mathrm{n}}{2}[2{\mathrm{a}}_1+(5\mathrm{n}-1\left)\mathrm{d}\right]}{\frac{\mathrm{n}}{2}[2{\mathrm{a}}_1+(\mathrm{n}-1\left)\mathrm{d}\right]}$

 $=\frac{5\left[\right(6-\mathrm{d})+5\mathrm{nd}]}{(6-\mathrm{d})+\mathrm{nd}}$

 $\because \frac{{\mathrm{S}}_{5\mathrm{n}}}{{\mathrm{S}}_{\mathrm{n}}}$ is independent of n so d = 6

So a₂ = a₁ + d = 3 + 6 = 9

*           The most appropriate answer to this question is (9), but because of ambiguity in language, IIT has declared (3, 9 ; 3 & 9 both) as correct answer.