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Grade: 10
        
If m times the nth term of an AP is equal to n times of n term and m is not equal to n.so that its (m+n)th term is zero.
9 months ago

Answers : (1)

Arun
13861 Points
							
Dear student
 

Let mth term be am  and  nth term be an 

According to the question :

m(am ) = n(an )

Apply Formula : an = 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 + (m2 - m) d }= [na + (n2 - n) d]

{ma + (m2 d- md) }= [na + (n2 d- nd) ]

[ma-na] + { m d-  nd } + (nd-md) = 0

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

Apply : a -  b2 = (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 

So  :the (m+n)th  term of the A.P is zero

 

 

Regards

Arun (askIITians forum expert)

9 months ago
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