If m times of mth term is equal to n times of nth term then find value of (m+n)th term
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Answer:
m*tm=n*tn
Step-by-step explanation:
m*[a+(m-1)d]=n*[a+(n-1)d]
m*[a+md-d]=n*[a+nd-d]
am+m²d-md=an+n²d-nd
am-an+m²d-n²d-md+nd=0
a(m-n)+d(m²-n²)-d(m-n)=0
a(m-n)+d(m-n)(m+n)-d(m-n)=0
dividing by(m-n) since m≠n
a+d(m+n)-d=0
a+d(m+n-1)=0
a+(m+n-1)d=0...........1
tm+n=a+(m+n-1)d
tm+n=0........... from 1
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