Question

prove that f (n)=an+b is a.p. where a and b are constants

Answer 1

Th terms of this function are

f(0) = b  f(1) = a+b  f(2) = 2a+b,............f(x)=ax+b , f(x+1) = a(x+1)+b , ...........

f(x+1) - f(x) = a which is constant and is called common difference.

Hence the given series is in A.P