Calculate the explicit formula

Calculate term number 15

And the Sum of the first 15 terms for:

2,4,6,8,10

a_{n} = a_{1} + (n - 1)d

d = Δ between consecutive terms

d = a_{n} - a_{n - 1}

We see a common difference = 2

We have a_{1} = 2

**a _{n} = 2 + 2(n - 1)**

Plug in n = 6 and d = 2

a_{6} = 2 + 2(6 - 1)

a_{6} = 2 + 2(6 - 1)

a_{6} = 2 + 2(5)

a_{6} = 2 + 10

a_{6} = 12

Plug in n = 7 and d = 2

a_{7} = 2 + 2(7 - 1)

a_{7} = 2 + 2(7 - 1)

a_{7} = 2 + 2(6)

a_{7} = 2 + 12

a_{7} = 14

Plug in n = 8 and d = 2

a_{8} = 2 + 2(8 - 1)

a_{8} = 2 + 2(8 - 1)

a_{8} = 2 + 2(7)

a_{8} = 2 + 14

a_{8} = 16

Plug in n = 9 and d = 2

a_{9} = 2 + 2(9 - 1)

a_{9} = 2 + 2(9 - 1)

a_{9} = 2 + 2(8)

a_{9} = 2 + 16

a_{9} = 18

Plug in n = 10 and d = 2

a_{10} = 2 + 2(10 - 1)

a_{10} = 2 + 2(10 - 1)

a_{10} = 2 + 2(9)

a_{10} = 2 + 18

a_{10} = 20

Plug in n = 11 and d = 2

a_{11} = 2 + 2(11 - 1)

a_{11} = 2 + 2(11 - 1)

a_{11} = 2 + 2(10)

a_{11} = 2 + 20

a_{11} = 22

Plug in n = 12 and d = 2

a_{12} = 2 + 2(12 - 1)

a_{12} = 2 + 2(12 - 1)

a_{12} = 2 + 2(11)

a_{12} = 2 + 22

a_{12} = 24

Plug in n = 13 and d = 2

a_{13} = 2 + 2(13 - 1)

a_{13} = 2 + 2(13 - 1)

a_{13} = 2 + 2(12)

a_{13} = 2 + 24

a_{13} = 26

Plug in n = 14 and d = 2

a_{14} = 2 + 2(14 - 1)

a_{14} = 2 + 2(14 - 1)

a_{14} = 2 + 2(13)

a_{14} = 2 + 26

a_{14} = 28

Plug in n = 15 and d = 2

a_{15} = 2 + 2(15 - 1)

a_{15} = 2 + 2(15 - 1)

a_{15} = 2 + 2(14)

a_{15} = 2 + 28

a_{15} = 30

S_{n} = Sum of the first n terms

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

2 |

S_{15} = | 15(a_{1} + a_{15}) |

2 |

S_{15} = | 15(2 + 30) |

2 |

S_{15} = | 15(32) |

2 |

S_{15} = | 480 |

2 |

S_{15} = **240**

S_{15} = **240**

Free Arithmetic and Geometric and Harmonic Sequences Calculator - This will take an arithmetic series or geometric series or harmonic series, and an optional amount (n), and determine the following information about the sequence

1) Explicit Formula

2) The remaining terms of the sequence up to (n)

3) The sum of the first (n) terms of the sequence Also known as arithmetic sequence, geometric sequence, and harmonic sequence

This calculator has 4 inputs.

1) Explicit Formula

2) The remaining terms of the sequence up to (n)

3) The sum of the first (n) terms of the sequence Also known as arithmetic sequence, geometric sequence, and harmonic sequence

This calculator has 4 inputs.

- arithmetic and geometric and harmonic sequences
- difference
- the result of one of the important mathematical operations, which is obtained by subtracting two numbers
- formula
- a fact or a rule written with mathematical symbols. A concise way of expressing information symbolically.
- sequence
- an arrangement of numbers or collection or objects in a particular order
- series
- the cumulative sum of a given sequence of terms

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