If two rods of lengths L and 2 L , having coefficients of linear expansion α and 2 α respectively…

$∆{\delta }_L=\alpha ∆TL$

$∆{\delta }_{2L}=\left(2\alpha \right)∆T\left(2L\right)$

The rods are connected end to end means in series, therefore, net change in length after the composition of rods, $\Rightarrow ∆{\delta }_{net}=∆{\delta }_L+∆{\delta }_{2L}=\alpha ∆TL+4\alpha ∆TL=5\alpha ∆TL$

$$\begin{gathered} \Rightarrow ∆{\delta }_{net}={\alpha }_{eff}∆T\left(3L\right)=∆{\delta }_L+∆{\delta }_{2L} \\ \Rightarrow {\alpha }_{eff}∆T\left(3L\right)=5\alpha ∆TL \\ \Rightarrow {\alpha }_{eff}=\frac{5\alpha }{3} \end{gathered}$$