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Complete the recursive formula of the arithmetic sequence 
0,11,22,33,dots.

c(1)=

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

Complete the recursive formula of the arithmetic sequence 0,11,22,33, 0,11,22,33, \ldots ..\newline c(1) = \(\square\) \newline c(n) = c(n-1)+\(\square\)

Full solution

Q. Complete the recursive formula of the arithmetic sequence 0,11,22,33, 0,11,22,33, \ldots ..\newline c(1) = \(\square\) \newline c(n) = c(n-1)+\(\square\)
  1. Identify First Term: Identify the first term of the sequence. The first term in the sequence is 00. This will be our c(1)c(1).
  2. Determine Common Difference: Determine the common difference between consecutive terms. By subtracting the first term from the second term, we find that the common difference is 1111 (since 110=1111 - 0 = 11).
  3. Write Recursive Formula: Write the recursive formula using the first term and the common difference. The recursive formula for an arithmetic sequence is c(n)=c(n1)+dc(n) = c(n-1) + d, where dd is the common difference. Since we have determined that the first term c(1)c(1) is 00 and the common difference dd is 1111, we can write the recursive formula as follows:\newlinec(1)=0c(1) = 0\newlinec(n)=c(n1)+11c(n) = c(n-1) + 11 for n > 1

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