It has been given that a, b, and c are in an arithmetic progression. Let a=x−p,b=x, and c=x+p We know that a, b, and c are real numbers. Therefore, the arithmetic mean of a,b,c should be greater than or equal to the geometric mean.
a+b+c
3
≥3√abc
a+b+c
3
≥3√4
3x
3
≥3√4 x≥3√4 We know that x=b Therefore,b≥3√4 or b≥2