For some positive integer n, the expansion of (1-x)^n has three consecutive coefficients a, b, and c that satisfy 1:7:35 What must n be?

For some positive integer n, the expansion of (1-x)^n has three consecutive coefficients a, b, and c that satisfy 1:7:35 What must n be?

Hello Guest!

\(\large n=7\)

\((1-x)^{\color{blue}7}={\color{blue}1}\cdot (-x^7)+{\color{blue}7}x^6+{\color{blue}35}x^4-21x^5-35x^3+21x^2-7x+1\)

  !