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`        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

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] + { m2  d-  n2 d } + (nd-md) = 0a*[m-n] + d* { m2  -  n2  } + d* (n-m) = 0Apply : a2  -  b2 = (a+b) (a-b)a*[m-n] + d* { (m+n) (m-n) } - d* (m - n) = 0Divide the above equation  with " (m-n)" ,We get :a + d* { (m+n) } - d = 0a + { (m+n) - 1 } d = 0COMPARING 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  RegardsArun (askIITians forum expert)
```
9 months ago
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