Question

can any body tell how to do it

Answer 1

I know the answer but it's explanation is very very big and typing such a long answer only for 5 points it is my loss.

m + n = 0

Answer 2

Answer:

(m + n)th = 0

Step-by-step explanation:

We know that,

AP = a + (n-1) *d

[ a - first term , d -Common Difference ,n - No of terms ]

m( a + (m-1) d ) = n( a + (n-1) d )

{ma + (2m - m) d } = [na + (2n - n) d]

{ma + (2md- md) } = [na + (2nd- nd) ]

[ma-na] + { 2md - 2nd } + (nd - md) = 0

a*[m-n] + d* { 2m  -  2n  } + d* (n-m) = 0

Apply : 2a  -  2b = (a+b) (a-b)

a*[m-n] + d* { (m+n) (m-n) } - d* (m - n) = 0

Divide the above equation  with " (m-n)" ,

We get ,

a + d* { (m+n) } - d = 0

a + { (m+n) - 1 } d = 0

COMPARING THE EQUATION WITH : an = a + (n-1) d  

Therefore : a + { (m+n) - 1 } d  = am+n  

So : am+n  = 0  

Hence, (m+n)th term of an AP is zero.