Find the two consecutive terms in the expansion of $(3+2x{)}^{74}$ so that the coefficients of power of x are equal.

$$\begin{gathered} T_{r+1}{=}^{74}{C}_r{3}^{74-r}(2x{)}^r \\ andthen{T}_{r+2}{=}^{74}{C}_{r+1}{3}^{73-r}(2x{)}^{r+1} \\ asco-efficientsareequal{}^{74}{C}_r{3}^{73-r}{2}^r{=}^{74}{C}_{r+1}{3}^{73-r}{2}^{r+1} \\ (\frac{74!}{74-r}!r!)\times =(\frac{74!}{(73-r)!(r+1)!})\times 2 \\ 3(73-r)!(r+1)!=2(74-r)!r! \\ =3(73-r)!(r+1)!=2(74-r)!(73-r)!r! \\ =3(r+1)=2(74-r) \\ =3r+3=148-2r \\ \therefore 5r=148-3 \\ r=(\frac{145}{5})=29 \\ Hencetermsare(29+1{)}^{th}and(29+2{)}^{nd} \\ or30^{th}and31^{th}term \end{gathered}$$