Question

The value of x from which 2x, (x + 10) and (3 x + 2) are consecutive terms of an AP is​

Answer 1

Answer:

Value of x = 6

Step-by-step explanation:

Given:

• Three terms in an A.P 2x, x + 10 and 3x + 2

To find:

• The value of x so that the 3 terms are in A.P

Concept:

Here if the 3 terms are in A.P, the common difference between them must be same. Equating it we get the value of x.

Solution:

Let the first term be a = 2x

Let the second term be b = x + 10

Let the third term be c = 3x + 2

If the 3 terms are in A.P the common difference between them must be same.

Hence,

b - a = c - b

b + b = c + a

b = a + c/2---------(1)

Substitute the value in equation 1

x + 10 = (2x + 3x + 2)/2

x + 10 = (5x + 2)/2

2 (x + 10) = 5x + 2

2x + 20 = 5x + 2

5x - 2x = 20 - 2

3x = 18

 x = 18/3

x = 6

Hence the value of x so that the the terms are in A.P is 6

$\boxed{\bold{Value\:of\:x=6}}$

Verification:

First term = 2x = 2 × 6 = 12

Second term = x + 10 = 6 + 10 = 16

Third term = 3x + 2 = 3 × 6 + 2 = 20

If the terms are in A.P then,

16 - 12 = 20 - 16

4 = 4

Hence verified.