Question

If 3+x,x-3,-2x+12 are in A.P., then value of x is: *

I

Answer 1

Answer:

The value of x is 7

Step-by-step explanation:

Since the given numbers are in AP

a₂ - a₁ = a₂

(x - 3) - ( 3 + x) = (-2x + 12) - (x - 3)

-6 = -3x + 15

3x = 21

x = 7

Answer 2

The value of $x$ will be 7.

Given,

$(3 + x), (x - 3), (-2x + 12)$ are in A. P.

To find,

x.

Solution,

An Arithmetic Progression or A. P. is defined as a series of numbers in which the difference between two consecutive terms is always constant. This difference is called the common difference.

When the terms $a,b, c$ are in A. P. then, the common difference is $(b-a)$ or $(c-b)$ and both will be equal, so,

$b-a=c-b$

Or,

$2b =a+c$     ...(1)

Here, the given terms are,

$3 + x,$ $x - 3,$ and $-2x + 12$.

Say,

$a=3 + x,\\b=x - 3,and \\c=-2x + 12$

Now, using eq. (1),

$2(x-3)=(3+x)+(-2x+12)$

$\implies 2x-6=3+x-2x+12$

$\implies 2x-6=3-x+12$

$\implies 2x+x=3+6+12$

$\implies 3x=21$

⇒ x = 7.

Therefore, the value of $x$ will be 7.