SOLUTION: If (x+1), (-2x+4) and (x+15) are 3 consecutive terms of an arithmetic sequence, determine x and the next 2 terms.

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Question 1015023: If (x+1), (-2x+4) and (x+15) are 3 consecutive terms of an arithmetic sequence, determine x and the next 2 terms.
Answer by ikleyn(52788) About Me  (Show Source):
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If (x+1), (-2x+4) and (x+15) are 3 consecutive terms of an arithmetic sequence, determine x and the next 2 terms.
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In arithmetic progression the difference between consecutive terms is a constant value. 
So, make a difference of the second and first terms and equals it to the difference between the third and the second terms.

Your equation is 

(-2x +4) - (x+1) = (x+15) - (-2x+4).

Simplify and solve it:

-3x + 3 = 3x + 11,

-6x = 8,

x = -8%2F6 = -4%2F3.

The terms are 

1-st:  x+1 = -4%2F3%2B1 = -1%2F3,

2-nd:  -2x+4 = -2%2A%28-4%2F3%29%2B4 = 8%2F3%2B4 = 20%2F3,

3-rd:  x + 15 = -4%2F3%2B15 = 41%2F3.

These are really the terms of the arithmetic progression with the difference 21%2F3 = 7.

Now you can easily calculate the 4-th and 5-th terms.