Name: Write the recursive equation for the sequences below. a. 1,4,7,10,13,dots

Identify Pattern: To find the recursive equation for the sequence, we first need to determine the pattern or rule that the sequence follows. We can do this by looking at the difference between consecutive terms.Calculate Differences: The difference between the first term (1) and the second term (4) is 3. Let's check if this difference is consistent throughout the sequence. 4 - 1 = 3 7 - 4 = 3 10 - 7 = 3 13 - 10 = 3Determine Common Difference: Since the difference between consecutive terms is consistently 3, we can say that the sequence increases by 3 each time. This is the common difference for the arithmetic sequence.Write Recursive Equation: A recursive equation for an arithmetic sequence is typically written in the form: a_n = a_(n-1) + d, where a_n is the nth term, a_(n-1) is the previous term, and d is the common difference.Final Recursive Equation: Given that the first term a_1 is 1 and the common difference d is 3, the recursive equation for this sequence is: a_n = a_(n-1) + 3, for n > 1, with a_1 = 1.

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Write the recursive equation for the sequences below.
a.
1,4,7,10,13,dots

$\newline$ $1$ . Write the recursive equation for the sequences below. $\newline$ a. $1,4,7,10,13, \ldots$

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\newline

1

. Write the recursive equation for the sequences below.

\newline

1,4,7,10,13, \ldots

Identify Pattern: To find the recursive equation for the sequence, we first need to determine the pattern or rule that the sequence follows. We can do this by looking at the difference between consecutive terms.
Calculate Differences: The difference between the first term ( $1$ ) and the second term ( $4$ ) is $3$ . Let's check if this difference is consistent throughout the sequence. $\newline$ $4 - 1 = 3$ $\newline$ $7 - 4 = 3$ $\newline$ $10 - 7 = 3$ $\newline$ $13 - 10 = 3$
Determine Common Difference: Since the difference between consecutive terms is consistently $3$ , we can say that the sequence increases by $3$ each time. This is the common difference for the arithmetic sequence.
Write Recursive Equation: A recursive equation for an arithmetic sequence is typically written in the form: $\newline$ $a_n = a_{n-1} + d$ , where $a_n$ is the $n$ th term, $a_{n-1}$ is the previous term, and $d$ is the common difference.
Final Recursive Equation: Given that the first term $a_1$ is $1$ and the common difference $d$ is $3$ , the recursive equation for this sequence is: $\newline$ $a_n = a_{n-1} + 3$ , for n > 1, with $a_1 = 1$ .