If the first, second and last terms of an A.P. are a, b and  2a respectively, then its sum is

Here a1 = a and a2 = b∴Common difference d = a2 – a1 = b – aLet n be the number of terms in the series∴ an=2a=a+(n−1)d or  (n−1)d=a or (n−1)(b−a)=a∴ n−1=ab−a or  n=ab−a+1=a+b−ab−a=bb−a∴ Sum =n2a1+an=b2(b−a)(a+2a)=3ab2(b−a).