Question

in ap multiplying by m with mth term and multiplying by n with nth term. let two terms are equal. find the (m+n)th term​

Answer 1

Answer:

to find:

a+(m+n-1)d

given:

m(a+(m-1)d)= n(a+(n-1)d

ma+ md(m-1)= na + nd(n-1)

ma-na +md(m-1) - nd(n-1)=0

a(m-n) + m^2d - md - n^2d +nd =0

a(m-n) + d(m^2-n^2 - m + n)=0

a(m-n) + d( (m+n) (m-n) - (m-n))=0          (using identity a^2-b^2=(a+b)(a-b))

a(m-n) + d ( (m-n)(m+n-1))=0

(m-n) (a+ (m+n-1)d)=0

a+(m+n-1)d = 0* (m-n)

HENCE,

a+(m+n-1)d=0