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Write the Nth Term of the a . P . 1 M , 1 + M M , 1 + 2 M M , . . . . - Mathematics

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Question

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

 
Sum
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Solution

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

 

 
 

 

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Chapter 5: Arithmetic Progression - Exercise 5.7 [Page 56]

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RD Sharma Mathematics [English] Class 10
Chapter 5 Arithmetic Progression
Exercise 5.7 | Q 18 | Page 56

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