hi,

can someone pls give a detailed , step by step answer for the given question ??

1. 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 )

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

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