Question

Find $x$ if $2x,x+10,3x+2$ are the consecutive terms in an AP.

• A. 6
• B. 3
• C. 1
• D. 9

Answer 1

The correct option is A

6

If three numbers a, A and b are in arithmetic progression, then A is the arithmetic mean between a and b.

i.e., A = $\frac{a+b}{2}$

Since $2x,x+10,3x+2$ are in AP, $x+10$ is the arithmetic mean of $2x$ and $3x+2$.

$\Rightarrow$ $x+10=\frac{2x+3x+2}{2}$

$\Rightarrow 2(x+10)=2x+(3x+2)$

$2x+20=5x+2$

$3x=18$

$x=6$.