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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 )

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 )

Grade:10

3 Answers

Vijay Mukati
askIITians Faculty 2590 Points
5 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
5 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
askIITians Faculty 2590 Points
5 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

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