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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=−19n−24a_n = -19n - 24\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=−19n−24a_n = -19n - 24\newlinean=_a_n = \_
  1. Write Sequence Terms: Write down the first few terms of the sequence by substituting n=1,2,3,4n = 1, 2, 3, 4 into the explicit formula an=−19n−24a_n = -19n - 24.
    a1=−19(1)−24=−43a_1 = -19(1) - 24 = -43
    a2=−19(2)−24=−62a_2 = -19(2) - 24 = -62
    a3=−19(3)−24=−81a_3 = -19(3) - 24 = -81
    a4=−19(4)−24=−100a_4 = -19(4) - 24 = -100
  2. Find Common Difference: Find the common difference dd between consecutive terms.d=a2−a1=−62−(−43)=−19d = a_2 - a_1 = -62 - (-43) = -19d=a3−a2=−81−(−62)=−19d = a_3 - a_2 = -81 - (-62) = -19d=a4−a3=−100−(−81)=−19d = a_4 - a_3 = -100 - (-81) = -19
  3. Recursive Formula: Write the recursive formula using the common difference. \newlinean=an−1+da_n = a_{n - 1} + d\newlineSince d=−19d = -19, the recursive formula is:\newlinean=an−1−19a_n = a_{n - 1} - 19

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