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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\newline13,6,1,8, 13,6,-1,-8, \ldots \text {. } \newline c(1) = \(\square\) \newline c(n) = c(n-1)+\(\square\)

Full solution

Q. Complete the recursive formula of the arithmetic sequence\newline13,6,1,8, 13,6,-1,-8, \ldots \text {. } \newline c(1) = \(\square\) \newline c(n) = c(n-1)+\(\square\)
  1. 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.\newlineCalculation: 613=76 - 13 = -7
  2. Write Recursive Formula: Now that we have the common difference, we can write the recursive formula. The first term of the sequence, c(1)c(1), is given as 1313. The recursive formula will express each term c(n)c(n) in terms of the previous term c(n1)c(n-1) plus the common difference.\newlineCalculation: c(n)=c(n1)+(7)c(n) = c(n-1) + (-7)
  3. Complete Recursive Formula: We can now write the complete recursive formula for the sequence. The first term is 1313, and each subsequent term is found by adding 7-7 to the previous term.\newlineFinal recursive formula: c(1)=13c(1) = 13, c(n)=c(n1)7c(n) = c(n-1) - 7

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