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Complete the recursive formula of the arithmetic sequence 1,15,29,43,dots".. " {:[a(1)=◻],[a(n)=a(n-1)+]:}

Complete the recursive formula of the arithmetic sequence 1,15,29,43,… 1,15,29,43, \ldots ..\newlinea(1)= a(1)= \newlinea(n)=a(n−1)+ a(n)=a(n-1)+

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Q. Complete the recursive formula of the arithmetic sequence 1,15,29,43,… 1,15,29,43, \ldots ..\newlinea(1)= a(1)= \newlinea(n)=a(n−1)+ a(n)=a(n-1)+
  1. Identify first term: Identify the first term of the sequence. The first term is given as 11.
  2. Determine common difference: Determine the common difference by subtracting the first term from the second term. The second term is 1515, so the common difference is 15−1=1415 - 1 = 14.
  3. Write recursive formula: Write the recursive formula using the first term and the common difference. The recursive formula for an arithmetic sequence is a(n)=a(n−1)+da(n) = a(n-1) + d, where dd is the common difference.
  4. Substitute values into formula: Substitute the first term and the common difference into the recursive formula. The first term a(1)a(1) is 11, and the common difference dd is 1414. Therefore, the recursive formula is a(n)=a(n−1)+14a(n) = a(n-1) + 14.

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