Question

The coefficients of second third fourth terms are in ap find n in (1+x)^n

Answer 1

Answer:

$terms = > \binom{n}{1} \: \: .\: \: \: \binom{n}{2} \: \: and \: \: \binom{n}{3} \\ \\ 2 \binom{n}{2} = \binom{n}{1} + \binom{n}{3} \\ \\ after \: \: solving \: \: this \: = > \\ \\ {n}^{2} - 9n + 14 = 0 \\ \\ {n}^{2} - 7n - 2n + 14 = 0 \\ \\ n(n - 7) - 2(n -7 ) = 0 \\ \\ (n - 2)(n - 7) = 0 \\ \\ n = 2 \: \: \: \: and \: \: \: \: n = 7$