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

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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.

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

Possible Answers:

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)

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)

Report an Error

Example Question #2 : 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,... )

Possible Answers:

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

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

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

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

f(n)=2-3(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)

Report an Error

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.

(4,6,8,10,... )

Possible Answers:

f(n)=4+(n-1)

f(n)=2+4(n-1)

f(n)=4+2(n-1)

f(n)=-4+2(n-1)

f(n)=4-2(n-1)

Correct answer:

f(n)=4+2(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.

$\\ \textup{Term}_1+d=\textup{Term}_2 \\d=6-4 \\d=2$

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

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

where

$\\A=4 \\d=2$

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

f(n)=4+2(n-1)

Report an Error

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.

(-1,-7,-13,-19,... )

Possible Answers:

f(n)=1+6(n-1)

f(n)=-1-8(n-1)

f(n)=1-6(n-1)

f(n)=-1-6(n-1)

f(n)=-1+6(n-1)

Correct answer:

f(n)=-1-6(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.

$\\ \textup{Term}_1+d=\textup{Term}_2 \\d=-7--1 \\d=-6$

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

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

where

$\\A=-1 \\d=-6$

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

f(n)=-1-6(n-1)

Report an Error

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.

(3,4,5,6,... )

Possible Answers:

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

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

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

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

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

Correct answer:

f(n)=3+1(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.

$\\ \textup{Term}_1+d=\textup{Term}_2 \\d=4-3 \\d=1$

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

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

where

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

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

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

Report an Error

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.

$\left(\frac{3}{4},\frac{1}{4},-\frac{1}{4},-\frac{3}{4},...\right)$

Possible Answers:

$f(n)=\frac{3}{4}-\frac{1}{4}(n-1)$

$f(n)=\frac{3}{2}-\frac{1}{4}(n-1)$

$f(n)=\frac{3}{2}-\frac{1}{2}(n-1)$

$f(n)=\frac{1}{2}-\frac{3}{4}(n-1)$

$f(n)=\frac{3}{4}-\frac{1}{2}(n-1)$

Correct answer:

$f(n)=\frac{3}{4}-\frac{1}{2}(n-1)$

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.

$\\ \textup{Term}_1+d=\textup{Term}_2 \\\\d=\frac{1}{4}-\frac{3}{4} \\\\d=-\frac{1}{2}$

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

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

where

$\\A=\frac{3}{4} \\\\d=-\frac{1}{2}$

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

$f(n)=\frac{3}{4}-\frac{1}{2}(n-1)$

Report an Error

Example Question #7 : 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.

(-2,3,8,13,... )

Possible Answers:

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

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

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

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

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

Correct answer:

f(n)=-2+5(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.

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

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

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

where

$\\A=-2 \\d=5$

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

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

Report an Error

Example Question #8 : 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.

$\left(\frac{1}{2},\frac{3}{2},\frac{5}{2},\frac{7}{2},... \right )$

Possible Answers:

$f(n)=1+\frac{1}{2}(n-1)$

$f(n)=\frac{1}{2}+1(n-1)$

$f(n)=\frac{1}{2}-1(n-1)$

$f(n)=\frac{1}{2}+1(n+1)$

$f(n)=-\frac{1}{2}+1(n-1)$

Correct answer:

$f(n)=\frac{1}{2}+1(n-1)$

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.

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

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

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

where

$\\A=\frac{1}{2} \\\\d=1$

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

$f(n)=\frac{1}{2}+1(n-1)$

Report an Error

Example Question #9 : 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.

(3,-1,-5,-9,... )

Possible Answers:

f(n)=3+4(n-1)

f(n)=3-4(n-1)

f(n)=-3-4(n-1)

f(n)=-4+3(n-1)

f(n)=4-3(n-1)

Correct answer:

f(n)=3-4(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.

$\\ \textup{Term}_1+d=\textup{Term}_2 \\d=-1-3 \\d=-4$

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

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

where

$\\A=3 \\d=-4$

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

f(n)=3-4(n-1)

Report an Error

Example Question #10 : 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.

(5,-5,-15,-25,... )

Possible Answers:

f(n)=-5-10(n-1)

f(n)=-5+10(n-1)

f(n)=5-10(n-1)

f(n)=10-5(n-1)

f(n)=5+10(n-1)

Correct answer:

f(n)=5-10(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.

$\\ \textup{Term}_1+d=\textup{Term}_2 \\d=-5-5 \\d=-10$

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

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

where

$\\A=5 \\d=-10$

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

f(n)=5-10(n-1)

Report an Error

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

Study concepts, example questions & explanations for Common Core: High School - Functions

All Common Core: High School - Functions Resources

Example Questions

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

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

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

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

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

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

Example Question #7 : Write, Model, And Translate Arithmetic And Geometric Sequences Recursively And Explicitly: Ccss.Math.Content.Hsf Bf.A.2

Example Question #8 : Write, Model, And Translate Arithmetic And Geometric Sequences Recursively And Explicitly: Ccss.Math.Content.Hsf Bf.A.2

Example Question #9 : Write, Model, And Translate Arithmetic And Geometric Sequences Recursively And Explicitly: Ccss.Math.Content.Hsf Bf.A.2

Example Question #10 : Write, Model, And Translate Arithmetic And Geometric Sequences Recursively And Explicitly: Ccss.Math.Content.Hsf Bf.A.2

All Common Core: High School - Functions Resources

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