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Complete the recursive formula of the arithmetic sequence 12,10,8,6,dots. b(1)= b(n)=b(n-1)+

Complete the recursive formula of the arithmetic sequence 12,10,8,6,… 12,10,8,6, \ldots .\newlineb(1)= b(1)= \newlineb(n)=b(n−1)+ b(n)=b(n-1)+

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Q. Complete the recursive formula of the arithmetic sequence 12,10,8,6,… 12,10,8,6, \ldots .\newlineb(1)= b(1)= \newlineb(n)=b(n−1)+ b(n)=b(n-1)+
  1. Identify pattern and common difference: Identify the pattern in the sequence to determine the common difference. The sequence is decreasing by 22 each time: 1212 to 1010, 1010 to 88, 88 to 66, and so on. This indicates that the common difference is −2-2.
  2. Write first term: Write the first term of the sequence. The first term, b(1)b(1), is the starting point of the sequence, which is 1212.
  3. Determine recursive formula: Determine the recursive formula that relates each term to the previous term. Since the common difference is −2-2, the recursive formula will subtract 22 from the previous term to get the next term. Therefore, the recursive formula is b(n)=b(n−1)−2b(n) = b(n-1) - 2.

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