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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=−5a_1 = -5 \newlinean=an−1+7a_n = a_{n - 1} + 7 \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=−5a_1 = -5 \newlinean=an−1+7a_n = a_{n - 1} + 7 \newlinean=_____a_n = \_\_\_\_\_
  1. Identify Sequence Type: Initial term is a1=−5a_1 = -5 and recursive formula is an=an−1+7a_n = a_{n - 1} + 7. This looks like an arithmetic sequence with a common difference of 77.
  2. Find Explicit Formula: To find the explicit formula for an arithmetic sequence, we use an=a1+(n−1)da_n = a_1 + (n - 1)d, where dd is the common difference.
  3. Substitute Values: Substitute a1=−5a_1 = -5 and d=7d = 7 into the formula: an=−5+(n−1)×7a_n = -5 + (n - 1) \times 7.
  4. Simplify Formula: Simplify the formula: an=−5+7n−7a_n = -5 + 7n - 7.
  5. Combine Like Terms: Combine like terms: an=7n−12an = 7n - 12.

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