If the coefficients of x^4, x^5 and x^6 in the expansion of (1+x)^n are in the arithmetic progression, then the maximum value of n is:

Step-by-step solution

aligned & Coeff. of x^4= ^n C₄ & Coeff. of x^5= ^n C₅ & Coeff. of x^6= ^n C₆ & ^n C₄, ^n C₅, ^n C₆ . A P & 2 C₅= ^n C₄+ ^n C₆ & 2= ^n C₄ ^n C₅ + ^n C₆ ^n C₅ ^n C_r ^n C_r = n-r+1 r & 2= 5 n-4 + n-5 6 & 12(n-4)=30+n^2-9 n+20 & n^2-21 n+98=0 & (n-14)(n-7)=0 & n_ =14 n_ =7 aligned