Question: If the coefficients of second, third and fourth term in the expansion of $(1 + x)^{2n}$ are in A.P...

Question

If the coefficients of second, third and fourth term in the expansion of $(1 + x)^{2n}$ are in A.P., then $2n^{2} - 9n + 7$ is equal to

Answer 1

$T_{2} =^{2n} ⥂ C_{1}$ , $T_{3} =^{2n} ⥂ C_{2},T_{4} =^{2n} ⥂ C_{3}$ are in A.P. then,

$2.^{2n} ⥂ C_{2} =^{2n} ⥂ C_{1} +^{2n} ⥂ C_{3}$

$2.\frac{2n(.2n - 1)}{2.1} = \frac{2n}{1} + \frac{2n(2n - 1)(2n - 2)}{3.2.1}$

On solving, $2n^{2} - 9n + 7 = 0$

Question: If the coefficients of second, third and fourth term in the expansion of \((1 + x)^{2n}\) are in A.P...