We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website.
Please click on "Accept cookies" if you agree to the setting of cookies. Cookies that do not require consent remain unaffected by this, see
cookie policy and privacy policy.
DECLINE COOKIES

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