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Use the initial term and the recursive formula to find an explicit formula for the sequence ana_n. Write your answer in simplest form.\newlinea1=43a_1 = 43\newlinean=an−1−5a_n = a_{n - 1} - 5\newlinean=_a_n = \_

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Q. Use the initial term and the recursive formula to find an explicit formula for the sequence ana_n. Write your answer in simplest form.\newlinea1=43a_1 = 43\newlinean=an−1−5a_n = a_{n - 1} - 5\newlinean=_a_n = \_
  1. Identify Initial Term: Initial term is a1=43a_1 = 43. Recursive formula is an=an−1−5a_n = a_{n - 1} - 5. This looks like an arithmetic sequence with a common difference of −5-5.
  2. Find Common Difference: Common difference dd is found by looking at the recursive formula: an=an−1−5a_n = a_{n - 1} - 5. So, d=−5d = -5.
  3. Use Explicit Formula: Explicit formula for an arithmetic sequence is an=a1+d(n−1)a_n = a_1 + d(n - 1). We plug in a1=43a_1 = 43 and d=−5d = -5 to get the explicit formula.
  4. Substitute Values: Substitute the values into the formula: an=43−5(n−1)a_n = 43 - 5(n - 1).
  5. Simplify Formula: Simplify the formula: an=43−5n+5a_n = 43 - 5n + 5.
  6. Combine Like Terms: Combine like terms: an=48−5nan = 48 - 5n.

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