Question

find the 6th term ofthe ap 2m+1/m,2m-1/m,2m-3/m​

Answer 1

Answer:

c.d=(2m-1/m)-(2m+1/m)

=2m-1/m-2m-1/m

=-2/m

6th term=(2m+1/m)+(6-1)(-2/m)

=(2m+1/m)-10/m

=2m-9/mAns

Answer 2

Given,

A.P. = 2m+1/m,2m-1/m,2m-3/m​

To Find,

The 6th term of the A.P. =?

Solution,

The given A.P. is 2m+1/m,2m-1/m,2m-3/m​.

The nth term of an A.P. is given by,

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

Where $T_{n} =$ nth term of the A.P.

             $a =$ first term

             $n =$ the term number

              $d =$ common difference

Here,

$a = 2m + \frac{1}{m}$

$n = 6$

To find $d$, we will find the difference between two consecutive terms.

Subtracting the first term from the second term to find the common difference,

$d = (2m - \frac{1}{m} ) - (2m + \frac{1}{m})$

   $= 2m - \frac{1}{m} - 2m - \frac{1}{m}$

    $= -\frac{2}{m}$

Therefore, the common difference between two terms is -2/m.

Substituting the values in the above formula to find the 6th term,

$T_{6} = 2m +\frac{1}{m} + ( 6 - 1)(-\frac{2}{m})$

     $= 2m + \frac{1}{m} - \frac{10}{m}$

      $= 2m - \frac{9}{m}$

Hence, the 6th term of the A.P. is $2m - \frac{9}{m}$.