If m times the mth term of an A P is equal to n times its nth term, show - Maths - Arithmetic Progressions

Question

If m times the mth term of an A P is equal to n times its nth
term, show that the (m+n)th term of the A P is zero (m ≠ n)

Priyanka Kedia · Accepted Answer

Let the first term and common difference of an A P be a and d respectively So, mth term of an A P is,

And nth term of an A P is,

Given that, m times the mth term of an A P is equal to n times its nth term, so,

Now,

Hence, the (m+n)th term of an A P is zero

If m times the mth term of an A.P. is equal to n times its nth term, show that the (m+n)th term of the A.P. is zero (m ≠ n).