Question

If mth term of an AP is n and nth term is m. Prove that (m+n)th will be zero.

Answer 1

SOLUTION

Let a be the first term and d be the

common difference.

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

=)a+(n-1)d = m................(2)

Subtracting Equation (2) from (1) we get

=) (m-n)d = n-m

=) d= -1

Putting this value in eq^n (1) we get

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

=) a-m +1= n or

=) a = m+n -1...........(3)

Now,

(m+n)th term am+n

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

=) a+ ad from (3)

=) a +a (-1) .....[d = -1]

=) a -a = 0

hope it helps ✔️

Answer 2

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