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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 ..\newline a(1)=\(\square\) \newline a(n)=a(n-1)+\(\square\)

Full solution

Q. Complete the recursive formula of the arithmetic sequence 1,15,29,43, 1,15,29,43, \ldots ..\newline a(1)=\(\square\) \newline a(n)=a(n-1)+\(\square\)
  1. Identify First Term: Identify the first term of the sequence. The first term in the sequence is given as 11.
  2. Determine Common Difference: Determine the common difference between consecutive terms. To find the common difference, subtract the first term from the second term: 151=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(n1)+da(n) = a(n-1) + d, where dd is the common difference. Since the first term a(1)a(1) is 11 and the common difference is 1414, the recursive formula is:\newlinea(1)=1a(1) = 1\newlinea(n)=a(n1)+14a(n) = a(n-1) + 14

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