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

Algebra ->  Sequences-and-series -> 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      Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!
Check your sequence again.
Should the third term be 24-x%5E2 or is it correct as is?

Answer by ikleyn(53937) About Me  (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, a%5B1%5D, a%5B2%5D, and a%5B3%5D, then

a%5B3%5D+-+a%5B2%5D = a%5B2%5D-a%5B1%5D.


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

24x+-+x%5E2 - %282x%5E2+%2B8%29%29 = %282x%5E2+%2B8%29%29 - %285x%2B2%29.


Now simplify and solve this quadratic equation for x.

Then restore the tree terms as the numbers, find a1%5D and the common difference.
Then find a%5B12%5D.

Good luck!