SOLUTION: Hey! So I was finishing up homework when yet another problem had me crying. After hours of trying to do it on my own, I decided to ask for help. Okay, so If 5x+2, 2x^2 + 8, 24x - x

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Question 1039332: Hey! So I was finishing up homework when yet another problem had me crying. After hours of trying to do it on my own, I decided to ask for help. Okay, so If 5x+2, 2x^2 + 8, 24x - x^2 form an arithmetic sequence, find x and the 12th term. I'm stumped trying to solve this. I literally have no idea. I tried subtracting the first term from the second to get the common difference, but hey, when I tried subtracting the third term from the second one, the "common" differences were not so common. Maybe the given is wrong? I don't know...
Found 2 solutions by Fombitz, ikleyn:
Answer by Fombitz(32388)   (Show Source): You can put this solution on YOUR website!
Check your sequence again.
Should the third term be or is it correct as is?

Answer by ikleyn(52782)   (Show Source): You can put this solution on YOUR website!
If 5x+2, 2x^2 + 8, 24x - x^2 form an arithmetic sequence, find x and the 12th term.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

If three terms form an arithmetic progression, , , and , then

 = .


Apply it to your three terms. You will get an equation 

 -  =  - .


Now simplify and solve this quadratic equation for x.

Then restore the tree terms as the numbers, find  and the common difference.
Then find .

Good luck!


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