Question

If m times of mth term is equal to n times of nth term then find value of (m+n)th term

Answer 1

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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