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,