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
+2440 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:
We can easily identify both of these with some observation. It is given that a1 =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. |
+2440 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:
We can easily identify both of these with some observation. It is given that a1 =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. |
