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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=36a_1 = 36\newlinean=an−1+13a_n = a_{n - 1} + 13\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=36a_1 = 36\newlinean=an−1+13a_n = a_{n - 1} + 13\newlinean=_____a_n = \_\_\_\_\_
  1. Identify Sequence Type: Initial term is a1=36a_1 = 36, and the recursive formula is an=an−1+13a_n = a_{n - 1} + 13. This looks like an arithmetic sequence with a common difference of 1313.
  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 the given values into the formula: an=36+(n−1)×13a_n = 36 + (n - 1) \times 13.
  4. Simplify Formula: Now, simplify the formula: an=36+13n−13a_n = 36 + 13n - 13.
  5. Combine Like Terms: Combine like terms: an=13n+36−13an = 13n + 36 - 13.
  6. Final Simplification: Final simplification gives us: an=13n+23a_n = 13n + 23.

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