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

Let , rth,(r+1)th and (r+2)th be three consecutive terms in the expansion of (1+x)n+5It is given that  n+5Cr−1:n+5Cr:n+5Cr+1=5:10:14⇒ n+5Cr 1+3Cr−1=105 and   n+5Cr+1 n+5Cr=1410⇒n+5−r+1r=2  and n+5−rr+1=75 ⇒n−3r+6=0  and 5n−12r+18=0 ⇒n=6,r=4