If n times the nth term of an ap is equal to m times the mth term, prove that it's (m+n)th term is equal to zero.
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If n times the nth term of an ap is equal to m times the mth term, prove that it's (m+n)th term is equal to zero.
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Answer:
nth term of AP =t
n
=a+(n−1)d
mth term of AP =t
m
=a+(m−1)d
⇒mt
m
=nt
n
m[a+(m−1)d]=n[a+(n−1)d]
m[a+(m−1)d]−n[a+(n−1)d]=0
a(m−n)+d[(m+n)(m−n)−(m−n)]=0
(m−n)[a+d((m+n)−1)]=0
a+[(m+n)−1]d=0
But t
m+n
=a+[(m+n)−1]d
∴t
m+n
=0