Question

If 2x, x+10, 3x+2 are in AP find value of x

Answer 1

S3 in AP is 2x+X+10+3x+2 =6x+12...(1)

S3=3/2 (2(2x)+2(X+10))...(2)

Equal both

(1)=(2)

3(X+10) =6(X+2)

3x+30=6x+12

3x-6x=12-30

-3x=-18

X=6

Answer 2

Answer:

6 is the correct answer.

☸Given☸

2x, x+10, 3x+2 are in A.P.

To Find:

• Value of x.

✯Solution✯

We know that,

• If a, b, c are in A.P. , then they must follow the condition 2b=a+c.

Similarly, it is given that  2x, x+10, 3x+2 are in A.P.

So,

$\longrightarrow\sf{2(x+10)=2x+3x+2}$

$\longrightarrow\sf{2x+20=5x+2}$

$\longrightarrow\sf{5x-2x=20-2}$

$\longrightarrow\sf{3x=18}$

$\longrightarrow\sf{x=\dfrac{18}{3}}$

$\longrightarrow\sf{\pink{x=6}}$

Hence, the value of x is $\bf{\green{6}}$.

$\boxed{\begin{minipage}{6.3cm}\sf{\orange{Properties of A.P.} -\\ \blue{1) If a constant term is added or subtracted from each term of an A.P. , then the resulting sequence is also an A.P. with the same common difference.\\ 2) If each term of given A.P. is multiplied or divided by a non-zero constant k, then the resulting sequence is also an A.P. with common difference kd or d/k, where d is the common differnce of the given A.P. }}\end{minipage}}$