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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=−21a_1 = -21\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=−21a_1 = -21\newlinean=an−1+11a_n = a_{n - 1} + 11\newlinean=_____a_n = \_\_\_\_\_
  1. Initial Term: The initial term is a1=−21a_1 = -21.
  2. Recursive Formula: The recursive formula is an=an−1+11a_n = a_{n - 1} + 11.
  3. Find Explicit Formula: To find the explicit formula, we need to express ana_n in terms of nn using the initial term and the common difference.
  4. Common Difference: The common difference is 1111, since each term is 1111 more than the previous term.
  5. Explicit Formula: The explicit formula for an arithmetic sequence is an=a1+(n−1)da_n = a_1 + (n - 1)d, where dd is the common difference.
  6. Substitute Values: Substitute a1=−21a_1 = -21 and d=11d = 11 into the formula: an=−21+(n−1)×11a_n = -21 + (n - 1) \times 11.
  7. Simplify Formula: Simplify the formula: an=−21+11n−11a_n = -21 + 11n - 11.
  8. Combine Like Terms: Combine like terms: an=11n−32an = 11n - 32.

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