Question

Write the value of x for which 2x, x + 10 and 3x + 2 are in A.P.

Answer 1

Here, we are given three terms,

First term (a₁) = 2x

Second term (a₂) = x + 10 

Third term (a₃) = 3x + 2

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

d = a₂ - a₁

d = (x + 10) - (2x)

d = x + 10 - 2x

d = 10 - x                                  ...............(1)

Also,

d = a₃ - a₂

d = (3x + 2) - (x + 10)

d = 3x + 2 - x -10

d = 2x - 8                                   ................(2) 

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

10 - x = 2x - 8

2x + x = 10 + 8 

3x = 18

x = `18/3`

x = 6

Therefore, for x = 6, these three terms will form an A.P.