Question

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

Answer 1

Given

x + 1 ,3x and 4x + 2 are in A.P.

To Find

the value of x.

Concept

• A.P. stands for arithmetic progression. For example :- 3,7,11,15 .....are in A.P.

• a,b and c are said to be in A.P. if 2b = a + c.

Calculations

Here, x + 1 ,3x and 4x + 2 will be in A.P. if and only if

2(3x) = (x + 1) + (4x + 2)

=> 6x = 5x + 3

=> 6x - 5x = 3

=> x = 3.

Hence,the value of x is 3 .

Answer 2

Given ,

x + 1 , 3x and 4x + 2 are in AP

As we know that ,

The difference between two consecutive term of AP is constant

Thus ,

3x - (x + 1) = 4x + 2 - (3x)

3x - x - 1 = 4x + 2 - 3x

2x - 1 = x + 2

x = 3

$\therefore$ The value of x is 3

Extra Information :

$\star \: \: \tt a_{n} = a + (n - 1)d$

$\star \: \: \tt S_{n} = \frac{n}{2} (a + a_{n})$