if m times the mth term of an ap is equal to n times its nth term, show that (m+n)th term of ap is zero

Asked by surain bhandari | 9th Aug, 2010, 07:13: PM

Expert Answer:

Dear Student,
 
Thge general nth term of an AP is a + (n -1)d.
 
From the given conditions,
 
m (a + (m-1)d) = n( a + (n-1)d)
=> am + m2d - md = an + n2d - nd
=> a(m-n) + (m+n)(m-n)d - (m-n)d = 0
=> (m-n) ( a + (m+n-1)d ) = 0
 
Rejecting the non-trivial case of m=n, we assume that m and n are different.
=> ( a + (m + n - 1)d ) = 0
 
The LHS of this equation denotes the (m+n)th term of the AP, which is Zero.
 
 
Regards Topperlearing.

Answered by  | 9th Aug, 2010, 08:59: PM

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