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  • If m times the mth term of an AP is equal to n times its nth term, show that the (m + n)th term of the AP is zero.     

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

 

 

Answers (1)

\\m(a+(m-1)d)=n(a+(n-1)d)\\am+m^2d-md=an+n^2d-nd\\a(m-n)-d(m-n)=d(n^2-m^2)\\(m-n)(a-d)=(n+m)(n-m)d\\d-a=(m+n)d\\a+(m+n-1)d=0\\a_{m+n}=0

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Safeer PP

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