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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=47a_1 = 47\newlinean=an−1+2a_n = a_{n - 1} + 2\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=47a_1 = 47\newlinean=an−1+2a_n = a_{n - 1} + 2\newlinean=_____a_n = \_\_\_\_\_
  1. Identify Initial Term and Recursive Formula: Initial term is a1=47a_1 = 47, and the recursive formula is an=an−1+2a_n = a_{n-1} + 2. This is an arithmetic sequence with a common difference of 22.
  2. Arithmetic Sequence Common Difference: The explicit formula for an arithmetic sequence is an=a1+d(n−1)a_n = a_1 + d(n - 1), where dd is the common difference.
  3. Explicit Formula Substitution: Substitute a1=47a_1 = 47 and d=2d = 2 into the formula: an=47+2(n−1)a_n = 47 + 2(n - 1).
  4. Simplify Formula: Simplify the formula: an=47+2n−2a_n = 47 + 2n - 2.
  5. Combine Like Terms: Combine like terms: an=2n+45an = 2n + 45.

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