Question

If first term of an AP is a, second term is b and last term is c then show that the sum of all the terms is
(a+c)(b+c-2a)/2(b-a).

Answer 1

this is the required answer

Answer 2

Good morning Friends ❤❤

First term =a 
second term =b
last term =c
common difference=(b-a)
tn =a+(n-1) d

c=a+(n-1) d

(c-a)=(n-1)(b-a) 

(c-a)/(b-a)+1=n 

( c+b-2a)/(b-a)=n--------------------(1)
now ,
we know sum of n terms=n/2 (first term+last term)
put equation (1)value 
= (b+c-2a)/(b-a)(a+c)
hence Sn=[(b+c-2a)(c+a)/(b-a)]