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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. \newline a1=−22a_1 = -22 \newline an=an−1+19a_n = a_{n - 1} + 19 \newline an=_____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. \newline a1=−22a_1 = -22 \newline an=an−1+19a_n = a_{n - 1} + 19 \newline an=_____a_n = \_\_\_\_\_
  1. Identify Sequence Type: Initial term is a1=−22a_1 = -22, and the recursive formula is an=an−1+19a_n = a_{n - 1} + 19. This looks like an arithmetic sequence with a common difference of 1919.
  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=−22a_1 = -22 and d=19d = 19 into the formula: an=−22+(n−1)×19a_n = -22 + (n - 1) \times 19.
  4. Simplify Formula: Now, simplify the formula: an=−22+19n−19a_n = -22 + 19n - 19.
  5. Combine Like Terms: Combine like terms: an=19n−41an = 19n - 41.

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