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All Common Core: High School - Functions Resources

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Flashcards: 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.

(1,-2,-5,-8,... )

f(n)=1+3(n-1)

f(n)=1+3(n+1)

f(n)=1-3(n+1)

f(n)=-1+3(n-1)

f(n)=1-3(n-1)

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Flashcards: 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.

(1,-2,-5,-8,... )

Your answer:

f(n)=1+3(n-1)

Your answer:

f(n)=1+3(n+1)

Your answer:

f(n)=1-3(n+1)

Your answer:

f(n)=-1+3(n-1)

Correct answer:

f(n)=1-3(n-1)

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.

$\\ \textup{Term}_1+d=\textup{Term}_2 \\d=\textup{Term}_2-\textup{Term}_1$

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

f(n)=A+d(n-1)

where

$\\ A=\textup{1}^{st} \textup{ term} \\d=\textup{difference constant} \\n=\textup{desired term}$

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.

$\\ \textup{Term}_1+d=\textup{Term}_2 \\d=-2-1 \\d=-3$

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

f(n)=A+d(n-1)

where

$\\A=1 \\d=-3$

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

f(n)=1-3(n-1)

Flashcards: 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.

(2,5,8,11,... )

f(n)=2+3(n-1)

f(n)=2+5(n-1)

f(n)=2-3(n-1)

f(n)=-2+5(n-1)

f(n)=2+1(n-1)

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Flashcards: 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.

(2,5,8,11,... )

Your answer:

f(n)=2+5(n-1)

Your answer:

f(n)=2-3(n-1)

Your answer:

f(n)=-2+5(n-1)

Your answer:

f(n)=2+1(n-1)

Correct answer:

f(n)=2+3(n-1)

Explanation:

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.

$\\ \textup{Term}_1+d=\textup{Term}_2 \\d=\textup{Term}_2-\textup{Term}_1$

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

f(n)=A+d(n-1)

where

$\\ A=\textup{1}^{st} \textup{ term} \\d=\textup{difference constant} \\n=\textup{desired term}$

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.

$\\ \textup{Term}_1+d=\textup{Term}_2 \\d=5-2 \\d=3$

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

f(n)=A+d(n-1)

where

$\\A=2 \\d=3$

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

f(n)=2+3(n-1)

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All Common Core: High School - Functions Resources

Flashcards: Write, Model, and Translate Arithmetic and Geometric Sequences Recursively and Explicitly: CCSS.Math.Content.HSF-BF.A.2

Flashcards: Write, Model, and Translate Arithmetic and Geometric Sequences Recursively and Explicitly: CCSS.Math.Content.HSF-BF.A.2

Flashcards: Write, Model, and Translate Arithmetic and Geometric Sequences Recursively and Explicitly: CCSS.Math.Content.HSF-BF.A.2

Flashcards: Write, Model, and Translate Arithmetic and Geometric Sequences Recursively and Explicitly: CCSS.Math.Content.HSF-BF.A.2

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