Question 1039332
If 5x+2, 2x^2 + 8, 24x - x^2 form an arithmetic sequence, find x and the 12th term. 
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If three terms form an arithmetic progression, {{{a[1]}}}, {{{a[2]}}}, and {{{a[3]}}}, then

{{{a[3] - a[2]}}} = {{{a[2]-a[1]}}}.


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

{{{24x - x^2}}} - {{{(2x^2 +8))}}} = {{{(2x^2 +8))}}} - {{{(5x+2)}}}.


Now simplify and solve this quadratic equation for x.

Then restore the tree terms as the numbers, find {{{a1]}}} and the common difference.
Then find {{{a[12]}}}.

Good luck!
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