Find n , if nC4, nC5, nC6 are in A P - Maths - Permutations and Combinations

Question

Find n , if nC4, nC5,
nC6 are in A P

Brijendra P. · Accepted Answer

Given C4n, C5n, C6n, are in A P
So 2C5n=C4n+C6n2×n!5!×n-5!=n!4!×n-4!+n!6!×n-6!25×4!×n-5×n-6!=14!×n-4×n-5×n-6!+16×5×4×4!n-6!25n-5=1n-4×n-5+16×5×41120=25n-5-1n-4×n-5=2n-8-15n-4×n-5n2-9n+20=48n-216n2-57n+236=0n = 57±572-4×2362=52
5, 4 49

Find n , if nC4, nC5, nC6 are in A.P.

Find n , if ⁿC4,ⁿC₅,ⁿC₆are in A.P.