Question

When the mth term of an arithmetic sequence is n and nth term is m what will be the common difference

Answer 1

Answer:

-1 is the common difference for the given problem

Answer 2

When the mth term of an arithmetic sequence is n and nth term is m, then the common difference will be -1.

Given:

$a_{m} = n$

$a_{n} = m$

To find:

Common difference = ?

Solution:

Arithmetic Progression - A sequence of series in which consecutive terms have constant difference.

$a_{m} = a + (m-1)d = n$

$a_{n} = a + ( n - 1 ) d = m$

$a + ( m - 1 ) d = n\\\\a + ( n - 1 ) d = m\\\\Subtraction\\\\(m-1)d - (n-1)d = n - m\\\\dm - d - dn + d = n - m\\\\(m-n)d = n - m\\\\d = -1$

Therefore, when the mth term of an arithmetic sequence is n and nth term is m, then the common difference will be -1.