# If #x+14, 13-x, x+8# is an arithmetic sequence, then what is the value of #x# ?

##### 2 Answers

#### Explanation:

The difference between

#(13x-1)-(x+14) = 12x-15#

The difference between

#(x+8) - (13x-1) = -12x+9#

The given terms form an arithmetic sequence if and only if these two differences are equal. That is:

#12x-15 = -12x+9#

Add

#24x=24#

Divide both sides by

#x=1#

So this is the only solution, yielding the arithmetic sequence:

#15, 12, 9#

As this gives a linear equation, there is only one solution.

#### Explanation:

If you know it is an arithmetic sequence, then you know that the common difference,