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

2 Answers
May 19, 2017

x=1

Explanation:

The difference between 13x-1 and x+14 is:

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

The difference between x+8 and 13x-1 is:

(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 12x+15 to both sides to get:

24x=24

Divide both sides by 24 to get:

x=1

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

15, 12, 9

May 21, 2017

x=1

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, d between any two consecutive terms is the same.

d= T_3-T_2= T_2-T_1

d = (x+8)- (13x-1)= (13x-1)-(x+14)

color(white)(............)x+8-13x+1 = 13x-1-x-14

color(white)(............................)9+15 = 12x+12x

color(white)(..................................)24 = 24x

color(white)(.....................................)1=x