Correct option: (c) 7 or 14
Explanation:
Coefficient of 5th, 6th, 7th term in A. P.
i.e. nc4, nc5, nc6 in A. P.
∴ nc4 + nc6 = 2 ∙ nc5
∴ [(n!) / {4!(n – 4)!}] + [(n!) / {6!(n – 6)!}] = 2 ∙ [(n!) / {5!(n – 5)!}]
∴ [{(n – 5)!} / {(n – 4)! 4!}] + [{(n – 5)!} / {(n – 6)! 6!}] = (2 / 5!)
∴ [1 / {(n – 4)4!}] + [(n – 5) / (6!)] = (2 / 5!)
∴ [5 / (n – 4)] + [(n – 5) / 6] = 2
∴ 30 + n2 – 4n – 5n + 20 = 12(n – 4)
∴ n2 – 9n + 50 = 12n – 48
∴ n2 – 21 + 98 = 0
n = 7, n = 14