For what values of n, nc1, nc2 and nc3 will be in arithmetic progression?

Dear Student,

Given, C1n, C2n and C3n are in A.P. So,2C2n=C1n+C3n2n!2!n-2!=n!1!n-1!+n!1!n-3!1n-2!=1n-1!+1n-3!1n-2n-3!=1n-1n-2n-3!+1n-3!1n-2=1n-1n-2+11=1n-2-1n-1n-21=n-1-1n-1n-21=1n-1n-1=1n=1+1n=2    Answer

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