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.

\(\displaystyle \\ \textup{Term}_1+d=\textup{Term}_2 \\d=\textup{Term}_2-\textup{Term}_1\)

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

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

where 

\(\displaystyle \\ A=\textup{1}^{st} \textup{ term} \\d=\textup{difference constant} \\n=\textup{desired term}\)

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.

\(\displaystyle \\ \textup{Term}_1+d=\textup{Term}_2 \\d=-2-1 \\d=-3\)

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

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

where 

\(\displaystyle \\A=1 \\d=-3\)

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

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

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.

\(\displaystyle \\ \textup{Term}_1+d=\textup{Term}_2 \\d=\textup{Term}_2-\textup{Term}_1\)

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

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

where 

\(\displaystyle \\ A=\textup{1}^{st} \textup{ term} \\d=\textup{difference constant} \\n=\textup{desired term}\)

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.

\(\displaystyle \\ \textup{Term}_1+d=\textup{Term}_2 \\d=5-2 \\d=3\)

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

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

where 

\(\displaystyle \\A=2 \\d=3\)

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

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

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.

\(\displaystyle \\ \textup{Term}_1+d=\textup{Term}_2 \\d=\textup{Term}_2-\textup{Term}_1\)

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

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

where 

\(\displaystyle \\ A=\textup{1}^{st} \textup{ term} \\d=\textup{difference constant} \\n=\textup{desired term}\)

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.

\(\displaystyle \\ \textup{Term}_1+d=\textup{Term}_2 \\d=6-4 \\d=2\)

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

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

where 

\(\displaystyle \\A=4 \\d=2\)

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

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

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.

\(\displaystyle \\ \textup{Term}_1+d=\textup{Term}_2 \\d=\textup{Term}_2-\textup{Term}_1\)

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

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

where 

\(\displaystyle \\ A=\textup{1}^{st} \textup{ term} \\d=\textup{difference constant} \\n=\textup{desired term}\)

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.

\(\displaystyle \\ \textup{Term}_1+d=\textup{Term}_2 \\d=-7--1 \\d=-6\)

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

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

where 

\(\displaystyle \\A=-1 \\d=-6\)

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

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

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.

\(\displaystyle \\ \textup{Term}_1+d=\textup{Term}_2 \\d=\textup{Term}_2-\textup{Term}_1\)

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

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

where 

\(\displaystyle \\ A=\textup{1}^{st} \textup{ term} \\d=\textup{difference constant} \\n=\textup{desired term}\)

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.

\(\displaystyle \\ \textup{Term}_1+d=\textup{Term}_2 \\d=4-3 \\d=1\)

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

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

where 

\(\displaystyle \\A=3 \\d=1\)

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

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

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.

\(\displaystyle \\ \textup{Term}_1+d=\textup{Term}_2 \\d=\textup{Term}_2-\textup{Term}_1\)

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

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

where 

\(\displaystyle \\ A=\textup{1}^{st} \textup{ term} \\d=\textup{difference constant} \\n=\textup{desired term}\)

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.

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

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

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

where 

\(\displaystyle \\A=\frac{3}{4} \\\\d=-\frac{1}{2}\)

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

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

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.

\(\displaystyle \\ \textup{Term}_1+d=\textup{Term}_2 \\d=\textup{Term}_2-\textup{Term}_1\)

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

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

where 

\(\displaystyle \\ A=\textup{1}^{st} \textup{ term} \\d=\textup{difference constant} \\n=\textup{desired term}\)

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.

\(\displaystyle \\ \textup{Term}_1+d=\textup{Term}_2 \\d=3--2 \\d=5\)

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

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

where 

\(\displaystyle \\A=-2 \\d=5\)

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

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

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.

\(\displaystyle \\ \textup{Term}_1+d=\textup{Term}_2 \\d=\textup{Term}_2-\textup{Term}_1\)

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

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

where 

\(\displaystyle \\ A=\textup{1}^{st} \textup{ term} \\d=\textup{difference constant} \\n=\textup{desired term}\)

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.

\(\displaystyle \\ \textup{Term}_1+d=\textup{Term}_2 \\\\d=\frac{3}{2}-\frac{1}{2} \\\\d=1\)

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

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

where 

\(\displaystyle \\A=\frac{1}{2} \\\\d=1\)

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

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

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.

\(\displaystyle \\ \textup{Term}_1+d=\textup{Term}_2 \\d=\textup{Term}_2-\textup{Term}_1\)

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

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

where 

\(\displaystyle \\ A=\textup{1}^{st} \textup{ term} \\d=\textup{difference constant} \\n=\textup{desired term}\)

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.

\(\displaystyle \\ \textup{Term}_1+d=\textup{Term}_2 \\d=-1-3 \\d=-4\)

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

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

where 

\(\displaystyle \\A=3 \\d=-4\)

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

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

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.

\(\displaystyle \\ \textup{Term}_1+d=\textup{Term}_2 \\d=\textup{Term}_2-\textup{Term}_1\)

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

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

where 

\(\displaystyle \\ A=\textup{1}^{st} \textup{ term} \\d=\textup{difference constant} \\n=\textup{desired term}\)

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.

\(\displaystyle \\ \textup{Term}_1+d=\textup{Term}_2 \\d=-5-5 \\d=-10\)

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

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

where 

\(\displaystyle \\A=5 \\d=-10\)

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

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