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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

Best Answer 

 #1
avatar+2340 
+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(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
avatar+2340 
+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(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

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