ExplanationThe sequence \(S_n = S_{n – 1} + S_{n - 2} - 3\) can be read as “to get any term in sequence S, sum the two previous terms and subtract 3.”

The problem gives the first two terms and asks for the sixth term:

5 | 0 | | | | |

\(S_1\) | \(S_2\) | \(S_3\) | \(S_4\) | \(S_5\) | \(S_6\) |

To get any term, sum the two previous terms and subtract 3. So the third term will equal 5 + 0 – 3 = 2.

The fourth term will equal 0 + 2 – 3 = –1. The fifth term will equal 2 + (–1) – 3 = –2. The sixth term will equal –1 + (–2) – 3 = –6:

5 | 0 | 2 | -1 | -2 | -6 |

\(S_1\) | \(S_2\) | \(S_3\) | \(S_4\) | \(S_5\) | \(S_6\) |

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Sandy

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