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Complete the recursive formula of the arithmetic sequence

13,6,-1,-8,dots". "

c(1)=

c(n)=c(n-1)+

Complete the recursive formula of the arithmetic sequence $\newline$ $13,6,-1,-8, \ldots \text {. }$ $\newline$ c(1) = \(\square\) $\newline$ c(n) = c(n-1)+\(\square\)

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Write a formula for an arithmetic sequence

Full solution

Q. Complete the recursive formula of the arithmetic sequence

\newline

13,6,-1,-8, \ldots \text {. }

\newline

c(1) = \(\square\)

\newline

c(n) = c(n-1)+\(\square\)

Calculate Common Difference: To find the recursive formula for the arithmetic sequence, we first need to determine the common difference between consecutive terms. We do this by subtracting any term from the term that follows it. $\newline$ Calculation: $6 - 13 = -7$
Write Recursive Formula: Now that we have the common difference, we can write the recursive formula. The first term of the sequence, $c(1)$ , is given as $13$ . The recursive formula will express each term $c(n)$ in terms of the previous term $c(n-1)$ plus the common difference. $\newline$ Calculation: $c(n) = c(n-1) + (-7)$
Complete Recursive Formula: We can now write the complete recursive formula for the sequence. The first term is $13$ , and each subsequent term is found by adding $-7$ to the previous term. $\newline$ Final recursive formula: $c(1) = 13$ , $c(n) = c(n-1) - 7$

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