Question

if x+1 ,3x,4x+2 are in AP the sum of these number​

Answer 1

Answer is in the attachment.

Answer 2

Answer : 27

Let the first term be a.

Let the common difference be d.

1st term = a...(1)

2nd term = a+d...(2)

3rd term = a+2d...(3)

Adding 1st term and 3rd term we get:

a + (a+2d)

= 2a + 2d

= 2(a+d)

= 2 × 2nd term ( From (2) )

Thus, we can say that :

1st term + 3rd term= 2 × 2nd term

So,

Given AP :

x+1, 3x, 4x+2

Adding this,

x+1 + 4x+2 = 2 × 3x

=> 5x+3 = 6x

» x = 3

So the value of x is 3.

Putting value of x,

x + 1 = 4

3x = 9

4x + 2 = 14

Thus,

Their sum = 4 + 9 + 14 = 27

Answer : 27