The correct option is D 6
Let the three consecutive terms in (1+x)n+5 be tr,tr+1,tr+2 having coefficients
n+5Cr−1, n+5Cr, n+5Cr+1
Given,
n+5Cr−1, n+5Cr, n+5Cr+1=5:10:14
∴ n+5Crn+5Cr−1=105 and n+5Cr+1n+5Cr=1410⇒ n+5−(r−1)r=2 and n−r+5r+1=75
⇒ n – r + 6 = 2r and 5n – 5r + 25 = 7r + 7
⇒ n + 6 = 3r and 5n + 18 = 12r
∴ n+63=5n+1812
⇒ 4n + 24 = 5n + 18
⇒ n = 6