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Use the initial term and the recursive formula to find an explicit formula for the sequence aa. Write your answer in simplest form. \newlinea=57a = 57 \newlinea=a+8a = a + 8 \newlinea=a = ______

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Q. Use the initial term and the recursive formula to find an explicit formula for the sequence aa. Write your answer in simplest form. \newlinea=57a = 57 \newlinea=a+8a = a + 8 \newlinea=a = ______
  1. Identify terms and formula: Identify the initial term and the recursive formula.\newlineThe initial term is given as a=57a = 57. This is the first term of the sequence.\newlineThe recursive formula is given as a=a+8a = a + 8, which means each term is 88 more than the previous term.
  2. Recognize sequence pattern: Recognize the pattern of the sequence.\newlineSince the sequence starts at 5757 and each term increases by 88, this is an arithmetic sequence.\newlineThe common difference (the amount added to each term to get to the next term) is 88.
  3. Write explicit formula: Write the explicit formula for an arithmetic sequence.\newlineThe explicit formula for an arithmetic sequence is an=a1+(n−1)da_n = a_1 + (n - 1)d, where ana_n is the nth term, a1a_1 is the first term, nn is the term number, and dd is the common difference.
  4. Substitute values: Substitute the given values into the explicit formula.\newlineWe know that a1=57a_1 = 57 (the first term) and d=8d = 8 (the common difference).\newlineSo the explicit formula becomes an=57+(n−1)×8a_n = 57 + (n - 1) \times 8.
  5. Simplify formula: Simplify the explicit formula.\newlinean=57+8n−8a_n = 57 + 8n - 8\newlinean=57+8n−8a_n = 57 + 8n - 8 simplifies to an=49+8na_n = 49 + 8n.

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