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Sequence Analysis and General Term

Sequence Analysis and General Term

TGM Original

Study the following sequence:

\({8,\ 13,\ 18,\ 23,\ \ldots}\)

  1. Write down the next term in the sequence.
  2. Find the \({8}^{\mathrm{th}}\) term in the sequence.
  3. Write down an expression for the \({n}^{\mathrm{th}}\) term.
  4. Explain, with a reason, why \({255}\) is not in the sequence.

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Answer:(a) \(28\) (b) \(T_8=43\) (c) \(T_n=5n+3\) (d) \(255\) is not in the sequence because solving \(5n+3=255\) gives \(n=\frac{252}{5}\), which is not an integer.

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