Question

Find the common difference of the A.P. and write the next two terms  \[0, \frac{1}{4}, \frac{1}{2}, \frac{3}{4}, . . . \]

Answer 1

In this problem, we are given different A.P. and we need to find the common difference of the A.P., along with the next two terms.

  \[0, \frac{1}{4}, \frac{1}{2}, \frac{3}{4}, . . . \]

Here,

a₁ = 0 

a₂ = `1/4`

So, common difference of the A.P. (d) =  a₂ - a₁ 

_{`=1/4 -0`}

_`=1/4`

Also, we need to find the next two terms of A.P., which means we have to find the 5^thand 6^th term.

So, for fifth term,

`a_5 = a_1 + 4d`

     `= 0 + 4(1/4)`

       = 1

Similarly, we find the sixth term,

`a_6 = a_1 + 5d`

   `   = 0 +5(1/4)`

    `= 5/4`

Therefore, the common difference is  `d = 1/4`  and the next two terms of the A.P. are `a_5 = 1,a_6 = 5/4` .