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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=−3n−23a_n = -3n - 23\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=−3n−23a_n = -3n - 23\newlinean=_a_n = \_
  1. Find Terms of Sequence: First, let's find the first few terms of the sequence by plugging in n=1,2,3,4n = 1, 2, 3, 4 into the explicit formula an=−3n−23a_n = -3n - 23.
  2. Calculate Common Difference: For n=1n = 1: a1=−3(1)−23=−3−23=−26a_1 = -3(1) - 23 = -3 - 23 = -26. For n=2n = 2: a2=−3(2)−23=−6−23=−29a_2 = -3(2) - 23 = -6 - 23 = -29. For n=3n = 3: a3=−3(3)−23=−9−23=−32a_3 = -3(3) - 23 = -9 - 23 = -32. For n=4n = 4: a4=−3(4)−23=−12−23=−35a_4 = -3(4) - 23 = -12 - 23 = -35.
  3. Determine Recursive Formula: Now, let's find the common difference dd by subtracting consecutive terms: a2−a1a_2 - a_1, a3−a2a_3 - a_2, a4−a3a_4 - a_3.
  4. Determine Recursive Formula: Now, let's find the common difference dd by subtracting consecutive terms: a2−a1a_2 - a_1, a3−a2a_3 - a_2, a4−a3a_4 - a_3.a2−a1=−29−(−26)=−3a_2 - a_1 = -29 - (-26) = -3.a3−a2=−32−(−29)=−3a_3 - a_2 = -32 - (-29) = -3.a4−a3=−35−(−32)=−3a_4 - a_3 = -35 - (-32) = -3.
  5. Determine Recursive Formula: Now, let's find the common difference dd by subtracting consecutive terms: a2−a1a_2 - a_1, a3−a2a_3 - a_2, a4−a3a_4 - a_3.a2−a1=−29−(−26)=−3a_2 - a_1 = -29 - (-26) = -3.a3−a2=−32−(−29)=−3a_3 - a_2 = -32 - (-29) = -3.a4−a3=−35−(−32)=−3a_4 - a_3 = -35 - (-32) = -3.The common difference dd is −3-3. So, the recursive formula is an=an−1+da_n = a_{n-1} + d.
  6. Determine Recursive Formula: Now, let's find the common difference dd by subtracting consecutive terms: a2−a1a_2 - a_1, a3−a2a_3 - a_2, a4−a3a_4 - a_3.a2−a1=−29−(−26)=−3a_2 - a_1 = -29 - (-26) = -3.a3−a2=−32−(−29)=−3a_3 - a_2 = -32 - (-29) = -3.a4−a3=−35−(−32)=−3a_4 - a_3 = -35 - (-32) = -3.The common difference dd is −3-3. So, the recursive formula is an=an−1+da_n = a_{n-1} + d.Substitute a2−a1a_2 - a_100 into the recursive formula: a2−a1a_2 - a_111.

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