Calculate the explicit formula, term number 10, and the sum of the first 10 terms for the following arithmetic series:

{1,9,17,25,...}

The explicit formula for an arithmetic series is a

d represents the common difference between each term, a

Looking at all the terms, we see the common difference is 8, and we have a

Therefore, our explicit formula is

Using our explicit formula with n = 10 and d = 8, we have:

Term # | Math Step 1 | Math Step 2 | Math Step 3 | Term |
---|---|---|---|---|

5 | a_{5} = 1 + 8(5 - 1) | a_{5} = 1 + 8(4) | a_{5} = 1 + 32 | a_{5} = 33 |

6 | a_{6} = 1 + 8(6 - 1) | a_{6} = 1 + 8(5) | a_{6} = 1 + 40 | a_{6} = 41 |

7 | a_{7} = 1 + 8(7 - 1) | a_{7} = 1 + 8(6) | a_{7} = 1 + 48 | a_{7} = 49 |

8 | a_{8} = 1 + 8(8 - 1) | a_{8} = 1 + 8(7) | a_{8} = 1 + 56 | a_{8} = 57 |

9 | a_{9} = 1 + 8(9 - 1) | a_{9} = 1 + 8(8) | a_{9} = 1 + 64 | a_{9} = 65 |

10 | a_{10} = 1 + 8(10 - 1) | a_{10} = 1 + 8(9) | a_{10} = 1 + 72 | a_{10} = 73 |

S_{n} = | n(a_{1} + a_{n}) |

2 |

With n = 10, we get:

S_{10} = | 10(a_{1} + a_{10}) |

2 |

S_{10} = | 10(1 + 73) |

2 |

S_{10} = | 10(74) |

2 |

S_{10} = | 740 |

2 |

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