Question

Write the nth term of the \[A.P. \frac{1}{m}, \frac{1 + m}{m}, \frac{1 + 2m}{m}, . . . .\]

Answer 1

Given:

 \[A . P . \frac{1}{m}, \frac{1 + m}{m}, \frac{1 + 2m}{m}, . . . .\]

We know that the nth term of an AP is given by \[a_n = a + \left( n - 1 \right)d\]
In the given AP

\[a = \frac{1}{m}\]
\[d = \frac{1 + m}{m} - \frac{1}{m} = \frac{1 + m - 1}{m} = 1\]

Thus, the nth term of the given AP is

\[a_n = \frac{1}{m} + \left( n - 1 \right)1 = \frac{1 + \left( n - 1 \right)m}{m}\]