ExplanationThe sequence \(P_n = 10(P_{n – 1}) – 2\) can be read as “to get any term in sequence P, multiply the previous term by 10 and subtract 2.”

The problem gives the first term and asks for the fourth:

2 | | | |

\(P_1\) | \(P_2\) | \(P_3\) | \(P_4\) |

To get P2 , multiply 2 × 10, then subtract 2 to get 18. Continue this procedure to find each subsequent term (“to get any term in sequence P, multiply the previous term by 10 and subtract 2”). Therefore, P3 = 10(18) – 2 = 178. P4 = 10(178) – 2 = 1,778.

2 | 18 | 178 | 1778 |

\(P_1\) | \(P_2\) | \(P_3\) | \(P_4\) |

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Sandy

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