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Complete the recursive formula of the arithmetic sequence

{:[-15","-11","-7","-3","dots.],[c(1)=◻],[c(n)=c(n-1)+◻]:}

Complete the recursive formula of the arithmetic sequence $\{:[-15, -11, -7, -3, \dots], [c(1)=\square], [c(n)=c(n-1)+\square]:\}$

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Find higher derivatives of rational and radical functions

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Q. Complete the recursive formula of the arithmetic sequence

\{:[-15, -11, -7, -3, \dots], [c(1)=\square], [c(n)=c(n-1)+\square]:\}

Identify First Term: To find the first term of the arithmetic sequence, we look at the given sequence: ${-15, -11, -7, -3, \ldots}$ . The first term is clearly stated as $-15$ .
Determine Common Difference: The recursive formula for an arithmetic sequence is generally given by $c(n) = c(n-1) + d$ , where $d$ is the common difference between the terms. To find the common difference, we subtract any term from the term that follows it in the sequence.
Calculate Common Difference: Subtracting the first term from the second term: $-11 - (-15) = -11 + 15 = 4$ . This is the common difference.
Complete Recursive Formula: Now we can complete the recursive formula. The first term $c(1)$ is $-15$ , and the common difference $d$ is $4$ . Therefore, the recursive formula is $c(n) = c(n-1) + 4$ .

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