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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=−24a_1 = -24\newlinean=an−1+11a_n = a_{n - 1} + 11\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=−24a_1 = -24\newlinean=an−1+11a_n = a_{n - 1} + 11\newlinean=_____a_n = \_\_\_\_\_
  1. Identify Initial Term: Initial term is a1=−24a_1 = -24. Recursive formula is an=an−1+11a_n = a_{n-1} + 11. This looks like an arithmetic sequence with a common difference.
  2. Find Common Difference: Common difference dd can be found from the recursive formula. It's the number we add each time, so d=11d = 11.
  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=−24a_1 = -24 and d=11d = 11.
  4. Substitute Values: Substitute the values into the formula: an=−24+11(n−1)a_n = -24 + 11(n - 1).
  5. Simplify Formula: Simplify the formula: an=−24+11n−11a_n = -24 + 11n - 11.
  6. Combine Like Terms: Combine like terms: an=11n−35an = 11n - 35.

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