Question

If the first ,second and last term of the ap are m ,n and 2m respectively,

prove that their sum is :-

$\frac{2mn}{2(n - m)}$

Answer 1

Hey mate..
========

The solution is in the pic.

Hope it helps !!

Answer 2

Hi ,

It is given that

m , n and 2m are first term ( a ) , second term and last term of an A. P

Let number of terms = p

common difference ( d ) = a2 - a1

d = n - m

last term = first term + ( p - 1 ) d

2m = m + ( p - 1 ) ( n - m )

m = ( p - 1 ) ( n - m )

m = p ( n - m ) - 1( n - m )

m = p( n - m ) - n + m

n = p ( n - m )

p = n / ( n - m ) ----( 1 )

*******"***********************

sum of p terms = p/2[ first term + last term ]

***************************************

sum of the terms = S

S= [ n /2 ( n - m ) ] { m + 2m }

= 3mn /[ 2( n - m ) ]

I hope this helps you.

:)