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Use the explicit formula to find a recursive formula for the sequence ana_n. Write your answer in simplest form.\newlineThe recursive formula should depend on an−1a_{n - 1}.\newlinean=−7n+2a_n = -7n + 2\newlinean=_a_n = \_

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Q. Use the explicit formula to find a recursive formula for the sequence ana_n. Write your answer in simplest form.\newlineThe recursive formula should depend on an−1a_{n - 1}.\newlinean=−7n+2a_n = -7n + 2\newlinean=_a_n = \_
  1. Given Explicit Formula: The explicit formula is an=−7n+2a_n = -7n + 2. Let's find the first few terms by plugging in n=1,2,3n = 1, 2, 3.
  2. Finding First Few Terms: For n=1n = 1, a1=−7(1)+2=−5a_1 = -7(1) + 2 = -5. For n=2n = 2, a2=−7(2)+2=−12a_2 = -7(2) + 2 = -12. For n=3n = 3, a3=−7(3)+2=−19a_3 = -7(3) + 2 = -19.
  3. Identifying Common Difference: Notice that the difference between consecutive terms is −7-7. (a2−a1=−12−(−5)=−7,a3−a2=−19−(−12)=−7)(a_2 - a_1 = -12 - (-5) = -7, a_3 - a_2 = -19 - (-12) = -7).
  4. Recursive Formula: The recursive formula for an arithmetic sequence is an=an−1+da_n = a_{n-1} + d, where dd is the common difference. Here, d=−7d = -7.
  5. Final Recursive Formula: So, the recursive formula is an=an−1−7a_n = a_{n-1} - 7.

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