SOLUTION: Find the value of x so that x+1, 3x-2, and 4x+5 form an arithmetic sequence

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Question 725335: Find the value of x so that x+1, 3x-2, and 4x+5 form an arithmetic sequence
Answer by Edwin McCravy(20059) About Me  (Show Source):
You can put this solution on YOUR website!
1st term = x+1, 
2nd term = 3x-2, 
and 
3rd term = 4x+5

In order to form an arithmetic sequence, this must be true:

        %28matrix%282%2C1%2C2nd%2Cterm%29%29%22%22-%22%22%28matrix%282%2C1%2C1st%2Cterm%29%29%22%22=%22%22%28matrix%282%2C1%2C3rd%2Cterm%29%29%22%22-%22%22%28matrix%282%2C1%2C2nd%2Cterm%29%29

      (3x-2)-(x+1) = (4x+5)-(3x-2)
         
You solve that and get x=10.
So

1st term = x+1 = 10+1 = 11 
2nd term = 3x-2 = 3(10)-2 = 30-2 = 28 
and 
3rd term = 4x+5 = 4(10)+5 = 40+5 = 45

So the series is 11, 28, and 45.

Checking in

         %28matrix%282%2C1%2C2nd%2Cterm%29%29%22%22-%22%22%28matrix%282%2C1%2C1st%2Cterm%29%29%22%22=%22%22%28matrix%282%2C1%2C3rd%2Cterm%29%29%22%22-%22%22%28matrix%282%2C1%2C2nd%2Cterm%29%29

            28 - 11 = 45 - 28
                 17 = 17.

So the answer is correct with a common difference of d=17.

Edwin