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Use the explicit formula to find a recursive formula for the sequence aa. Write your answer in simplest form.\newlineThe recursive formula should depend on aa.\newlinea=−9n−5a = -9n - 5\newlinea=a = ______

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Q. Use the explicit formula to find a recursive formula for the sequence aa. Write your answer in simplest form.\newlineThe recursive formula should depend on aa.\newlinea=−9n−5a = -9n - 5\newlinea=a = ______
  1. Identify Sequence Type: Identify if the given sequence is geometric or arithmetic.\newlineThe explicit formula a=−9n−5a = -9n - 5 involves a linear term in nn without any exponents, indicating that the sequence is arithmetic.
  2. Find First Term: Find the first term of the sequence using the explicit formula.\newlineTo find the first term, substitute n=1n = 1 into the explicit formula:\newlinea1=−9(1)−5a_1 = -9(1) - 5\newline=−9−5= -9 - 5\newline=−14= -14
  3. Find Second Term: Find the second term of the sequence using the explicit formula.\newlineTo find the second term, substitute n=2n = 2 into the explicit formula:\newlinea2=−9(2)−5a_2 = -9(2) - 5\newline=−18−5= -18 - 5\newline=−23= -23
  4. Find Common Difference: Find the common difference in the arithmetic sequence.\newlineThe common difference dd can be found by subtracting the first term from the second term:\newlined=a2−a1d = a_2 - a_1\newline=−23−(−14)= -23 - (-14)\newline=−23+14= -23 + 14\newline=−9= -9
  5. Write Recursive Formula: Write the recursive formula by plugging in the value of the common difference.\newlineThe recursive formula for an arithmetic sequence is an=an−1+da_n = a_{n - 1} + d. Substitute −9-9 for dd in the formula:\newlinean=an−1−9a_n = a_{n - 1} - 9

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