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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,…-15, -11, -7, -3, \dots\newlinec(1)=□c(1)=\square\newlinec(n)=c(n−1)+□c(n)=c(n-1)+\square

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Q. Complete the recursive formula of the arithmetic sequence −15,−11,−7,−3,…-15, -11, -7, -3, \dots\newlinec(1)=□c(1)=\square\newlinec(n)=c(n−1)+□c(n)=c(n-1)+\square
  1. Identify First Term: To find the first term of the arithmetic sequence, we look at the given sequence: −15,−11,−7,−3,…{-15, -11, -7, -3, \ldots}. The first term is clearly stated as −15-15.
  2. Determine Common Difference: The recursive formula for an arithmetic sequence is generally given by c(n)=c(n−1)+dc(n) = c(n-1) + d, where dd 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.
  3. Calculate Common Difference: Subtracting the first term from the second term: −11−(−15)=−11+15=4-11 - (-15) = -11 + 15 = 4. This is the common difference.
  4. Complete Recursive Formula: Now we can complete the recursive formula. The first term c(1)c(1) is −15-15, and the common difference dd is 44. Therefore, the recursive formula is c(n)=c(n−1)+4c(n) = c(n-1) + 4.

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