If the coefficients of r-th and (r+1)-th term | vedclass

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(D) The $r$-th term in the expansion of $(3+7x)^{29}$ is $T_r = {}^{29}C_{r-1} (3)^{29-(r-1)} (7x)^{r-1}$. The coefficient is ${}^{29}C_{r-1} (3)^{30-

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$21$

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(D) The $r$-th term in the expansion of $(3+7x)^{29}$ is $T_r = {}^{29}C_{r-1} (3)^{29-(r-1)} (7x)^{r-1}$. The coefficient is ${}^{29}C_{r-1} (3)^{30-r} (7)^{r-1}$.The $(r+1)$-th term is $T_{r+1} = {}^{29}C_r (3)^{29-r} (7x)^r$. The coefficient is ${}^{29}C_r (3)^{29-r} (7)^r$.Given that the coefficients are equal:${}^{29}C_{r-1} (3)^{30-r} (7)^{r-1} = {}^{29}C_r (3)^{29-r} (7)^r$Divide both sides by ${}^{29}C_{r-1} (3)^{29-r} (7)^{r-1}$:$3 = {}^{29}C_r / {}^{29}C_{r-1} 	imes 7$Using the formula ${}^nC_r / {}^nC_{r-1} = (n-r+1)/r$:$3 = \frac{29-r+1}{r} 	imes 7$$3r = 7(30-r)$$3r = 210 - 7r$$10r = 210$$r = 21$

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

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