The third term of an arithmetic sequence is 20.6 and the seventh term is 45.8. Find the twentieth term.

9514 1404 393

  x ≈ −2.10487278573

Step-by-step explanation:

I find a graphing calculator to be a very useful tool for the purpose. It shows the only real root is irrational and gives an approximation as x=-2.105.

The calculator also provides the means to perform Newton's method iteration easily to refine the value of the root to full calculator precision.

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The Newton's method iterator for finding the next iteration of the root (x') is ...

  x' = x - f(x)/f'(x)

Starting with the approximation shown on the graph, it only takes two iterations to get the root to the full precision of the calculator.