Find a sum of ap whose first term a second term b and last term c

Question

Find a sum of an ap whose first term is a second term is b and last term is c

 

Answer 1

S_n = ½•n(a₁+a_n)

 

a_n = a₁ + (n-1)d   and   a₁ = a and d = b-a  and a_n = c

 

c = a + (n-1)(b-a)

 

Solve the above for n in terms of a,b,c.

 

Now you can substitute into the S_n formula (and have fun simplifying the result, involving a, b, c.