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

Tr+1=n+5Crxr3consecutive terms areTr,Tr+1,Tr+2∴Co efficients,Tr=n+5Cr𕒵Tr+1=n+5CrTr+2=n+5Cr+1A.T.PTr+1Tr=105=(n+5)!r!(n+5−r)!×(r𕒵)!(n+6−r)!(n+5)!⇒2=n+6−rr∴3r=n+6→1Tr+2Tr=1410=(n+5)!(r+1)!(n+4−r)!×r!(n+5−r)!(n+5)!⇒75=n+5−rr+1⇒7r+7=5n+25𕒹r⇒12r=5n+18→2∴4n+24=5n+18(From112r=4n+24)⇒n=6