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Finding a quadratic rule from second differences

Finding a quadratic rule from second differences

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The first five terms of a sequence are \(3,\ 2,\ 3,\ 6,\ 11\).

  1. Write down the next two terms.
  2. Find an expression for the \(n\)th term.
  3. Which term of the sequence is equal to 102?

Solution:

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Answer:(a) \(18,\ 27\) (b) \(T_n=n^2-4n+6\) (c) the 12th term

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