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

Binomial Theorem

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

ⁿC_r-1 : ⁿC_r : ⁿC_r+1 = 1:7:42

r/(n-r+1) = 1/7

8r = n + 1

(r+1)/(n-r) = 7/42 = 1/6

7r = n - 6

r = 7

The correct option is B.