solve this with full process on notebook
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the answer will be this. hope this helps you
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adeeba025:
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let d be the common difference of an AP
a be the first term
Am=a+(m-1)d
An=a+(n-1)d
now,m(a+(m-1)d)=n(a+(n-1)d)
ma+m(m-1)d=na+n(n-1)d
ma-na=n²d-nd-m²d+md
(m-n)a=(n²-m²)d+(m-n)d
(m-n)a=(m-n)d-(m²-n²)d
(m-n)a=(m-n)d-(m-n)(m+n)d
(m-n)a=m-n)(1-(m+n))d
(m-n)a/(m-n)=-(m+n-1)d
a+(m+n-1)d=0
hence (m+n)th term is 0
a be the first term
Am=a+(m-1)d
An=a+(n-1)d
now,m(a+(m-1)d)=n(a+(n-1)d)
ma+m(m-1)d=na+n(n-1)d
ma-na=n²d-nd-m²d+md
(m-n)a=(n²-m²)d+(m-n)d
(m-n)a=(m-n)d-(m²-n²)d
(m-n)a=(m-n)d-(m-n)(m+n)d
(m-n)a=m-n)(1-(m+n))d
(m-n)a/(m-n)=-(m+n-1)d
a+(m+n-1)d=0
hence (m+n)th term is 0
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