Find x if 2x,x+10,3x+2 are the consecutive terms in an AP.
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 = a+b2
Since 2x,x+10,3x+2 are in AP, x+10 is the arithmetic mean of 2x and 3x+2.
⇒ x+10=2x+3x+22
⇒2(x+10)=2x+(3x+2)
2x+20=5x+2
3x=18
x=6.