If-the-coefficient-of-r-th-and-r-1-th-terms-in-the-expansion-of-3-7x-29-are-equal-then-r-equals-

Question Number 18758 by 786786AM last updated on 29/Jul/17

If the coefficient of r^{th} and {(r + 1)}^{th} terms

in the expansion of {(3 + 7 x)}^{29} are equal,

then r equals

Answered by Tinkutara last updated on 29/Jul/17

T_{r + 1} =^{n} C_{r} 3^{r} 7^{n - r} x^{n - r}

T_{r} =^{n} C_{r - 1} 3^{r - 1} 7^{n - r + 1}

Now^{29} C_{r} 3^{r} 7^{29 - r} =^{29} C_{r - 1} 3^{r - 1} 7^{30 - r}

\Rightarrow 3^{29} C_{r} = 7^{29} C_{r - 1}

\frac{3}{7} = \frac{r (r - 1)! (29 - r)!}{(30 - r) (29 - r)! (r - 1)!}

90 - 3 r = 7 r

r = 9