Question

If m times the mth term of A.P. is equal to n time it's nth term . Show that ( m+n ) th term is zero .​

Answer 1

Solution

Given:-

• If m times the mth term of A.P. is equal to n time it's nth term

To Prove :-

• (m + n)th terms is zeroes

Explanation

Let,

• a be the first terms & d be the common Defference.

According to question

==> m × [a + (m -1)d] = n ×[a + (n-1)d]

==> ma + m²d - md = na + n²d - 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 cases, m = n, we assume that m & n are different .

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

The L.H.S. of the Equation denote the (m+n) th terms of AP .

That's Proved.

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