# Common Core: High School - Functions : Write, Model, and Translate Arithmetic and Geometric Sequences Recursively and Explicitly: CCSS.Math.Content.HSF-BF.A.2

## Example Questions

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### Example Question #31 : Building Functions

Write an explicit recursive function that describes the following sequence.

Explanation:

This question is testing one's ability to identify and understand an arithmetic sequence and create the recursive function. Recall that for a function to be recursive, it depends on the previous term in the sequence. It is also important to recall that the difference in an arithmetic sequence is just a constant.

For the purpose of Common Core Standards, writing arithmetic and geometric recursive and explicit sequences, falls within the Cluster A of build a function that models a relationship between two quantities concept (CCSS.Math.content.HSF.BF.A).

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify the arithmetic difference of the sequence.

Step 2: Identify the basic form for an arithmetic recursive sequence.

where

Step 3: Substitute known values into the form from Step 2.

Following the steps from above for this particular problem is as follows.

Step 1: Identify the arithmetic difference of the sequence.

Step 2: Identify the basic form for an arithmetic recursive sequence.

where

Step 3: Substitute known values into the form from Step 2.

### Example Question #32 : Building Functions

Write an explicit recursive function that describes the following sequence.

Explanation:

This question is testing one's ability to identify and understand an arithmetic sequence and create the recursive function. Recall that for a function to be recursive, it depends on the previous term in the sequence. It is also important to recall that the difference in an arithmetic sequence is just a constant.

For the purpose of Common Core Standards, writing arithmetic and geometric recursive and explicit sequences, falls within the Cluster A of build a function that models a relationship between two quantities concept (CCSS.Math.content.HSF.BF.A).

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify the arithmetic difference of the sequence.

Step 2: Identify the basic form for an arithmetic recursive sequence.

where

Step 3: Substitute known values into the form from Step 2.

Following the steps from above for this particular problem is as follows.

Step 1: Identify the arithmetic difference of the sequence.

Step 2: Identify the basic form for an arithmetic recursive sequence.

where

Step 3: Substitute known values into the form from Step 2.

### Example Question #33 : Building Functions

Write an explicit recursive function that describes the following sequence.

Explanation:

This question is testing one's ability to identify and understand an arithmetic sequence and create the recursive function. Recall that for a function to be recursive, it depends on the previous term in the sequence. It is also important to recall that the difference in an arithmetic sequence is just a constant.

For the purpose of Common Core Standards, writing arithmetic and geometric recursive and explicit sequences, falls within the Cluster A of build a function that models a relationship between two quantities concept (CCSS.Math.content.HSF.BF.A).

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify the arithmetic difference of the sequence.

Step 2: Identify the basic form for an arithmetic recursive sequence.

where

Step 3: Substitute known values into the form from Step 2.

Following the steps from above for this particular problem is as follows.

Step 1: Identify the arithmetic difference of the sequence.

Step 2: Identify the basic form for an arithmetic recursive sequence.

where

Step 3: Substitute known values into the form from Step 2.

### Example Question #34 : Building Functions

Write an explicit recursive function that describes the following sequence.

Explanation:

This question is testing one's ability to identify and understand an arithmetic sequence and create the recursive function. Recall that for a function to be recursive, it depends on the previous term in the sequence. It is also important to recall that the difference in an arithmetic sequence is just a constant.

For the purpose of Common Core Standards, writing arithmetic and geometric recursive and explicit sequences, falls within the Cluster A of build a function that models a relationship between two quantities concept (CCSS.Math.content.HSF.BF.A).

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify the arithmetic difference of the sequence.

Step 2: Identify the basic form for an arithmetic recursive sequence.

where

Step 3: Substitute known values into the form from Step 2.

Following the steps from above for this particular problem is as follows.

Step 1: Identify the arithmetic difference of the sequence.

Step 2: Identify the basic form for an arithmetic recursive sequence.

where

Step 3: Substitute known values into the form from Step 2.

### Example Question #1 : Write, Model, And Translate Arithmetic And Geometric Sequences Recursively And Explicitly: Ccss.Math.Content.Hsf Bf.A.2

Write an explicit recursive function that describes the following sequence.

Explanation:

This question is testing one's ability to identify and understand an arithmetic sequence and create the recursive function. Recall that for a function to be recursive, it depends on the previous term in the sequence. It is also important to recall that the difference in an arithmetic sequence is just a constant.

For the purpose of Common Core Standards, writing arithmetic and geometric recursive and explicit sequences, falls within the Cluster A of build a function that models a relationship between two quantities concept (CCSS.Math.content.HSF.BF.A).

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify the arithmetic difference of the sequence.

Step 2: Identify the basic form for an arithmetic recursive sequence.

where

Step 3: Substitute known values into the form from Step 2.

Following the steps from above for this particular problem is as follows.

Step 1: Identify the arithmetic difference of the sequence.

Step 2: Identify the basic form for an arithmetic recursive sequence.

where

Step 3: Substitute known values into the form from Step 2.

### Example Question #1 : Write, Model, And Translate Arithmetic And Geometric Sequences Recursively And Explicitly: Ccss.Math.Content.Hsf Bf.A.2

Write an explicit recursive function that describes the following sequence.

Explanation:

This question is testing one's ability to identify and understand an arithmetic sequence and create the recursive function. Recall that for a function to be recursive, it depends on the previous term in the sequence. It is also important to recall that the difference in an arithmetic sequence is just a constant.

For the purpose of Common Core Standards, writing arithmetic and geometric recursive and explicit sequences, falls within the Cluster A of build a function that models a relationship between two quantities concept (CCSS.Math.content.HSF.BF.A).

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify the arithmetic difference of the sequence.

Step 2: Identify the basic form for an arithmetic recursive sequence.

where

Step 3: Substitute known values into the form from Step 2.

Following the steps from above for this particular problem is as follows.

Step 1: Identify the arithmetic difference of the sequence.

Step 2: Identify the basic form for an arithmetic recursive sequence.

where

Step 3: Substitute known values into the form from Step 2.

### Example Question #3 : Write, Model, And Translate Arithmetic And Geometric Sequences Recursively And Explicitly: Ccss.Math.Content.Hsf Bf.A.2

Write an explicit recursive function that describes the following sequence.

Explanation:

This question is testing one's ability to identify and understand an arithmetic sequence and create the recursive function. Recall that for a function to be recursive, it depends on the previous term in the sequence. It is also important to recall that the difference in an arithmetic sequence is just a constant.

For the purpose of Common Core Standards, writing arithmetic and geometric recursive and explicit sequences, falls within the Cluster A of build a function that models a relationship between two quantities concept (CCSS.Math.content.HSF.BF.A).

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify the arithmetic difference of the sequence.

Step 2: Identify the basic form for an arithmetic recursive sequence.

where

Step 3: Substitute known values into the form from Step 2.

Following the steps from above for this particular problem is as follows.

Step 1: Identify the arithmetic difference of the sequence.

Step 2: Identify the basic form for an arithmetic recursive sequence.

where

Step 3: Substitute known values into the form from Step 2.

### Example Question #4 : Write, Model, And Translate Arithmetic And Geometric Sequences Recursively And Explicitly: Ccss.Math.Content.Hsf Bf.A.2

Write an explicit recursive function that describes the following sequence.

Explanation:

This question is testing one's ability to identify and understand an arithmetic sequence and create the recursive function. Recall that for a function to be recursive, it depends on the previous term in the sequence. It is also important to recall that the difference in an arithmetic sequence is just a constant.

For the purpose of Common Core Standards, writing arithmetic and geometric recursive and explicit sequences, falls within the Cluster A of build a function that models a relationship between two quantities concept (CCSS.Math.content.HSF.BF.A).

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify the arithmetic difference of the sequence.

Step 2: Identify the basic form for an arithmetic recursive sequence.

where

Step 3: Substitute known values into the form from Step 2.

Following the steps from above for this particular problem is as follows.

Step 1: Identify the arithmetic difference of the sequence.

Step 2: Identify the basic form for an arithmetic recursive sequence.

where

Step 3: Substitute known values into the form from Step 2.

### Example Question #5 : Write, Model, And Translate Arithmetic And Geometric Sequences Recursively And Explicitly: Ccss.Math.Content.Hsf Bf.A.2

Write an explicit recursive function that describes the following sequence.

Explanation:

This question is testing one's ability to identify and understand an arithmetic sequence and create the recursive function. Recall that for a function to be recursive, it depends on the previous term in the sequence. It is also important to recall that the difference in an arithmetic sequence is just a constant.

For the purpose of Common Core Standards, writing arithmetic and geometric recursive and explicit sequences, falls within the Cluster A of build a function that models a relationship between two quantities concept (CCSS.Math.content.HSF.BF.A).

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify the arithmetic difference of the sequence.

Step 2: Identify the basic form for an arithmetic recursive sequence.

where

Step 3: Substitute known values into the form from Step 2.

Following the steps from above for this particular problem is as follows.

Step 1: Identify the arithmetic difference of the sequence.

Step 2: Identify the basic form for an arithmetic recursive sequence.

where

Step 3: Substitute known values into the form from Step 2.

### Example Question #6 : Write, Model, And Translate Arithmetic And Geometric Sequences Recursively And Explicitly: Ccss.Math.Content.Hsf Bf.A.2

Write an explicit recursive function that describes the following sequence.

Explanation:

This question is testing one's ability to identify and understand an arithmetic sequence and create the recursive function. Recall that for a function to be recursive, it depends on the previous term in the sequence. It is also important to recall that the difference in an arithmetic sequence is just a constant.

For the purpose of Common Core Standards, writing arithmetic and geometric recursive and explicit sequences, falls within the Cluster A of build a function that models a relationship between two quantities concept (CCSS.Math.content.HSF.BF.A).

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify the arithmetic difference of the sequence.

Step 2: Identify the basic form for an arithmetic recursive sequence.

where

Step 3: Substitute known values into the form from Step 2.

Following the steps from above for this particular problem is as follows.

Step 1: Identify the arithmetic difference of the sequence.

Step 2: Identify the basic form for an arithmetic recursive sequence.

where

Step 3: Substitute known values into the form from Step 2.

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