Question

If x + 1, 3x and 4x + 2 are in A.P., find the value of x.

Answer 1

Here, we are given three terms which are in A.P.

First-term `(a_1) = x + 1`

Second term `(a_2) = 3x`

Third term `(a_3) = 4x + 2`

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

`d = a_2 - a_1`

d = (3x) - (x + 1)

d = 3x - x - 1

d = 2x - 1 .........(1)

Also

`d = a_3 - a_2`

d= (4x  + 2) - (3x)

d = 4x - 3x + 2

d = x + 2 ......(2)

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

2x - 1 = x + 2

2x - x = 2 + 1

x = 3

Therefore for x= 3 these three terms will form an A.P