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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=4n−23a_n = 4n - 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=4n−23a_n = 4n - 23\newlinean=_a_n = \_
  1. Substitute nn into formula: 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=4n−23a_n = 4n - 23.\newlinea1=4(1)−23=−19a_1 = 4(1) - 23 = -19\newlinea2=4(2)−23=−15a_2 = 4(2) - 23 = -15\newlinea3=4(3)−23=−11a_3 = 4(3) - 23 = -11\newlinea4=4(4)−23=−7a_4 = 4(4) - 23 = -7
  2. Identify common difference: Notice the common difference between consecutive terms. \newlinea2−a1=−15−(−19)=4a_2 - a_1 = -15 - (-19) = 4\newlinea3−a2=−11−(−15)=4a_3 - a_2 = -11 - (-15) = 4\newlinea4−a3=−7−(−11)=4a_4 - a_3 = -7 - (-11) = 4\newlineThe common difference dd is 44.
  3. Write recursive formula: Write the recursive formula using the common difference. \newlinean=an−1+da_n = a_{n-1} + d\newlineSince d=4d = 4, the recursive formula is:\newlinean=an−1+4a_n = a_{n-1} + 4

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