If the coefficients of $r^{th}$ and ${(r+1)}^{th}$ terms in the expansion of $(3+7x{)}^{29}$are equal, then $r$ equals

The general term $T_{r-1}$ in the expansion of $(3+7x{)}^{29}$

is 

$\left.T_{r+1}{=}^{29}{C}_r{3}^{29-r}(7x{)}^r=\left\{{ }^{29}{C}_r\times 3^{29-r}\times 7^r\right\}\right\}{x}^r$

$\therefore$     $a_r$ = Coefficient of ${(r +1)}^{th}$ term ${=}^{29}{C}_r\times 3^{29-r}\times 7^r$

Now, 

      $a_r=a_{r-1}$

$\begin{array}{l}\Rightarrow {}^{29}{C}_r\times 3^{29-r}\times 7^r{=}^{29}{C}_{r-1}\times 3^{30-r}\times 7^{r-1}\\ \Rightarrow \frac{{ }^{29}{C}_r}{{ }^{29}{C}_{r-1}}=\frac{3}{7}\Rightarrow \frac{30-r}{r}=\frac{3}{7}\Rightarrow r=21\end{array}$