Question

If `4/5` , a, 2 are three consecutive terms of an A.P., then find the value of a. 

Answer 1

Here, we are given three consecutive terms of an A.P.

First term (a₁) =  `4/5`

Second term (a₂) = a 

Third term (a₃) =  2  

We need to find the value of a. So, in an A.P. the difference of two adjacent terms is always constant. So, we get,

 d = a₂ - a₁ 

d = a - `4/5`                      ................(1)

Also,

d = a₃ - a₂

d = 2 -a                        ...................(2) 

Now, on equating (1) and (2), we get,

`a - 4/5 = 2 - a`

` a + a = 2 +4/5`

      `2a = (10 + 4)/5`

        `a = 14/10`

          `a = 7/5`

Therefore,  `a = 7/5`