Question

if x+1, 3x and 4x+2 are three consecutive terms of an AP find the value of x.

Answer 1

Let the first term be a.

Let the common difference be d.

1st term = a...............(1)

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

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

Adding 1st term and 3rd term we get:

a+a+2d

=2a+2d

=2(a+d)

=2*2nd term[See(2)]

1st term+3rd term=2*2nd term

That is true for all AP.

So guess I got this.

Given your AP is:

x+1          ,             3x,                    4x+2

x+1+4x+2=2*3x

=5x+3=6x

Subtracting both sides by 5x we get:

5x-5x+3=6x-5x

That gives us:

3=x

x=3

So the value of x is 3.

Hope it helps you.

#Be brainly.

Answer 2

Answer:

x = 3

Step-by-step explanation:

x + 1, 3x and 4x + 2 are in A.P. So, the common difference between the consecutive terms should be the same. 3x – x – 1 = 4x + 2 – 3x ⇒ 2x – 1 = x + 2 ⇒ 2x – x = 2 + 1 ⇒ x = 3

Therefore, x = 3