Question

Find n , if n C4, n C5, n C6 are in A.P.​

Answer 1

It is given that C(n,4) and C(n,5) and C(n,6) are in A.P. where C(n,r)=

The three numbers a,b,c are in A.P then , → 2 b = a+c

→ 2 C(n,5) = C(n,4) + C(n,6)

→C(n,5) -C(n,4) =C(n,6) - C(n,5)

→

Cancelling n! from numerator, we get

and (n-5)!=(n-5)(n-6)! and (n-4)!=(n-4)(n-5)(n-6)! and 6!=6×5×4 and 5!=5×4!

Also ,Cancelling (n-6)! and 4! from denominator

→

→

m

→n²-21 n + 98 =0

→(n-14)(n-7)=0

n=14  or n=7