If 24, x, and 6 form the first three terms of an arithmetic sequence then which of the following is the value of x?
(1) 12
(3) 20
(2) 15
(4) 42

Work Shown:

d = common difference

p = first term = 24

q = second term = a+d = 24+d

r = third term = q+d = 24+d+d = 24+2d = 6

Solve for d

24+2d = 6

2d = 6-24

2d = -18

d = -18/2

d = -9

We add -9 to each term to get the next term. This is the same as subtracting 9 from each term to get the next term.

First term = 24

Second term = 24-9 = 15

Third term = 15-9 = 6

We get the sequence 24, 15, 6

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the correct answer is c

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