Question

Mth term of an A.P is n and the nth term isM.Show that (m+n)the term is zero

Answer 1

Answer:

from the condition it is given that

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

am+m^2d-md=na+n^2d-nd

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

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

rejecting the non trivial case of m=n we assume that m and n are different

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

now the LHS of this equation denotes that m+n the term of the AP which is zero