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# I NEED HELP ASAP!!!!!

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1143
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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

Apr 27, 2018

#1
+2339
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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(the first term)
• d (the common difference)

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.
Apr 28, 2018

#1
+2339
+3

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(the first term)
• d (the common difference)

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.
TheXSquaredFactor Apr 28, 2018