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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=−11n−35a_n = -11n - 35\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=−11n−35a_n = -11n - 35\newlinean=_a_n = \_
  1. Find First Few Terms: The explicit formula is an=−11n−35a_n = -11n - 35. Let's find the first few terms by plugging in n=1,2,3,4n = 1, 2, 3, 4.
  2. Calculate Terms for n=1,2,3,4n=1,2,3,4: For n=1n = 1, a1=−11(1)−35=−46a_1 = -11(1) - 35 = -46. For n=2n = 2, a2=−11(2)−35=−57a_2 = -11(2) - 35 = -57. For n=3n = 3, a3=−11(3)−35=−68a_3 = -11(3) - 35 = -68. For n=4n = 4, a4=−11(4)−35=−79a_4 = -11(4) - 35 = -79.
  3. Identify Common Difference: We notice that the sequence decreases by 1111 each time, so the common difference dd is −11-11.
  4. Recursive Formula: The recursive formula for an arithmetic sequence is an=an−1+da_n = a_{n-1} + d. Here, d=−11d = -11.
  5. Final Recursive Formula: So the recursive formula is an=an−1−11a_n = a_{n-1} - 11.

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