Complete the recursive formula of the arithmetic sequence {:[-3","-1","1","3","dots],[b(1)=],[b(n)=b(n-1)+]:}

Identify Pattern: Identify the pattern in the sequence to determine the common difference. The sequence given is -3, -1, 1, 3, ... . To find the common difference, subtract the first term from the second term: -1 - (-3) = -1 + 3 = 2. The common difference is 2.Recognize Formula: Recognize that a recursive formula for an arithmetic sequence has the form b(n) = b(n-1) + d, where d is the common difference. We have already determined that the common difference d is 2.Write Recursive Formula: Write the recursive formula using the common difference and the first term of the sequence. The first term b(1) is given as -3. Therefore, the recursive formula is b(n) = b(n-1) + 2.Check Formula: Check the recursive formula by applying it to find the second term from the first term. Using b(n) = b(n-1) + 2, we get b(2) = b(1) + 2 = -3 + 2 = -1, which matches the second term of the sequence.

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Complete the recursive formula of the arithmetic sequence

{:[-3","-1","1","3","dots],[b(1)=],[b(n)=b(n-1)+]:}

Complete the recursive formula of the arithmetic sequence $\newline$ $\begin{array}{l} -3,-1,1,3, \ldots \\ b(1)=\square \\ b(n)=b(n-1)+\square\\ \end{array}$

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Algebra 2

Write a formula for an arithmetic sequence

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Q. Complete the recursive formula of the arithmetic sequence

\newline

\begin{array}{l} -3,-1,1,3, \ldots \\ b(1)=\square \\ b(n)=b(n-1)+\square\\ \end{array}

Identify Pattern: Identify the pattern in the sequence to determine the common difference. The sequence given is $-3, -1, 1, 3, ext{...}$ . To find the common difference, subtract the first term from the second term: $-1 - (-3) = -1 + 3 = 2$ . The common difference is $2$ .
Recognize Formula: Recognize that a recursive formula for an arithmetic sequence has the form $b(n) = b(n-1) + d$ , where $d$ is the common difference. We have already determined that the common difference $d$ is $2$ .
Write Recursive Formula: Write the recursive formula using the common difference and the first term of the sequence. The first term $b(1)$ is given as $-3$ . Therefore, the recursive formula is $b(n) = b(n-1) + 2$ .
Check Formula: Check the recursive formula by applying it to find the second term from the first term. Using $b(n) = b(n-1) + 2$ , we get $b(2) = b(1) + 2 = -3 + 2 = -1$ , which matches the second term of the sequence.