The coefficients of three consecutive terms of (1 + x)n+5 are in the ratio 5 : 10 : 14. Then n = __________.

Let Tr-1, Tr, Tr+1 are three consecutive terms of (1 + x)n+5Tr−1=n+5Cr−2(x)r−2,Tr=n+5Cr−1xr−1,Tr+1=n+5Crxr,where,  n+5Cr−2:n+5Cr−1:n+5Cr=5:10:14.So  n+5Cr−25= n+5Cr−110= n+5Cr14Comparing first two results we have n - 3r = - 9        (1)Comparing last two results we have 5n - 12r = - 30   (2)From equation (1) and (2), n = 6