The recursive rule for a sequence is shown.

an=an−1+9

a1=21

What is the explicit rule for this sequence?

an=9n+12

an=12n+9

an=9n−12

an=12n−9

Guest Apr 27, 2018

#1**+2 **

11A recursive rule allows one to generate future terms of a sequence if one knows one or more of the previous terms. We know that the explicit rule can be written in the following form:

\(a_n=a_1+d(n-1)\)

There are two variables that we must identify in order to finish this formula. Those are:

- a
_{1 }(the first term) - d (the common difference)

We can easily identify both of these with some observation. It is given that a_{1} =21 since that information was given in the recursive formula. In the recursive formula, one must add 9 to obtain the next term in the sequence. This would be the common difference. Let's fill that in and simplify completely.

\(a_n=a_1+d(n-1)\) | Substitute in the known values and simplify. |

\(a_n=21+9(n-1)\) | Distribute the 9 into the binomial. |

\(a_n=21+9n-9\) | Combine like terms. |

\(a_n=9n+12\) | This answer corresponds to the first answer choice. |

TheXSquaredFactor
Apr 28, 2018

#1**+2 **

Best Answer

11A recursive rule allows one to generate future terms of a sequence if one knows one or more of the previous terms. We know that the explicit rule can be written in the following form:

\(a_n=a_1+d(n-1)\)

There are two variables that we must identify in order to finish this formula. Those are:

- a
_{1 }(the first term) - d (the common difference)

We can easily identify both of these with some observation. It is given that a_{1} =21 since that information was given in the recursive formula. In the recursive formula, one must add 9 to obtain the next term in the sequence. This would be the common difference. Let's fill that in and simplify completely.

\(a_n=a_1+d(n-1)\) | Substitute in the known values and simplify. |

\(a_n=21+9(n-1)\) | Distribute the 9 into the binomial. |

\(a_n=21+9n-9\) | Combine like terms. |

\(a_n=9n+12\) | This answer corresponds to the first answer choice. |

TheXSquaredFactor
Apr 28, 2018