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Use the explicit formula to find a recursive formula for the sequence an a_n . Write your answer in simplest form. The recursive formula should depend on an−1 a_{n - 1} . an=n+4 a_n = n + 4 an= a_n = ______

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Q. Use the explicit formula to find a recursive formula for the sequence an a_n . Write your answer in simplest form. The recursive formula should depend on an−1 a_{n - 1} . an=n+4 a_n = n + 4 an= a_n = ______
  1. Given Explicit Formula: The explicit formula is an=n+4a_n = n + 4. Let's find the first few terms by plugging in n=1,2,3,4n = 1, 2, 3, 4.
  2. Finding First Few Terms: For n=1n = 1, a1=1+4=5a_1 = 1 + 4 = 5. For n=2n = 2, a2=2+4=6a_2 = 2 + 4 = 6. For n=3n = 3, a3=3+4=7a_3 = 3 + 4 = 7. For n=4n = 4, a4=4+4=8a_4 = 4 + 4 = 8.
  3. Identifying Common Difference: We notice that each term is 11 more than the previous term, so the common difference dd is 11.
  4. Recursive Formula for Arithmetic Sequence: The recursive formula for an arithmetic sequence is an=an−1+da_n = a_{n - 1} + d. Here, d=1d = 1.
  5. Final Recursive Formula: So the recursive formula is an=an−1+1a_n = a_{n - 1} + 1.

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