if m times the m term of an arithmetic progression is equal to the n times n term then show that (M + n) terms of an arithmetic progression is zero
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m(a+(m-1)d)=n(a+(n-1) d)
am+m^2 d-md=an+n^2 d-nd
a(m-n) +(m-n) (m+n) d-(m-n) d=0
(m-n) (a+(m+n-1)d)=0
Therefore
m+nth term is 0
am+m^2 d-md=an+n^2 d-nd
a(m-n) +(m-n) (m+n) d-(m-n) d=0
(m-n) (a+(m+n-1)d)=0
Therefore
m+nth term is 0
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