If coefficients of three successive terms in binomial expansion of (1 + x)^n are in ratio 1 : 7 : 42

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7.Binomial Theorem

hard

If the coefficients of the three successive terms in the binomial expansion of $(1 + x)^n$ are in the ratio $1 : 7 : 42,$ then the first of these terms in the expansion is

$8^{th}$

$6^{th}$

$7^{th}$

$9^{th}$

(JEE MAIN-2015)

Solution

$\frac{^{\mathrm{n}} \mathrm{C}_{\mathrm{r}}}{1}=\frac{^{\mathrm{n}} \mathrm{C}_{\mathrm{r}+1}}{7}=\frac{^{\mathrm{n}} \mathrm{C}_{\mathrm{r}+2}}{42}$

By solving we get $r=6$

so, it is $7^{\text {th }}$ term

Standard 11

Mathematics

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hard

(JEE MAIN-2019)

If the coefficients of the three successive terms in the binomial expansion of $(1 + x)^n$ are in the ratio $1 : 7 : 42,$ then the first of these terms in the expansion is

Solution

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