# hi,can someone pls give a detailed , step by step answer for the given question ?? show that the sum of an a.p whose first term is a, second term is b, and the last term is c is equal to--                              (a+c) * (b+c-2a) / 2(b-a )

Vijay Mukati
7 years ago
Dear Student,

As the sum of n terms of an AP whose, first term is a an last terms is l is given by:

S = (n/2)(a + l)

We have, first term = a, second term = b and last term = c
using a, b, and c find the number of terms, as we know that,
c = a + (n-1)(b-a) from here find thevalue of n and just replace in above formula to calculate the sum of terms in an AP.

Best of Luck!
Vijay
DAN BROWN
37 Points
7 years ago
hello sir,
i tried doing what you asked, but am still not getting it. pls help.
( instead of writing, if you culd send a pic it would help me understand better.)

regards,
dan brown ( i do not wish to reveal my name )

Vijay Mukati
7 years ago
on simplifying, c = a + (n-1)(b-a) we get,

n = (c + b – 2a)/(b-a)

Now this value of n in S = n/2*(a + c)
we get, S = (a + c)*(c + b -2a)/2(b-a)

I hope the steps are clear now.

Thanks. Vijay