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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=−7n−1a = -7n - 1\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=−7n−1a = -7n - 1\newlinea=a = ______
  1. Identify Sequence Type: Identify if the given sequence is geometric or arithmetic.\newlineThe explicit formula a=−7n−1a = -7n - 1 does not involve any exponent terms, which indicates 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, we substitute n=1n = 1 into the explicit formula:\newlinea1=−7(1)−1a_1 = -7(1) - 1\newline=−7−1= -7 - 1\newline=−8= -8
  3. Find Second Term: Find the second term of the sequence using the explicit formula.\newlineTo find the second term, we substitute n=2n = 2 into the explicit formula:\newlinea2=−7(2)−1a_2 = -7(2) - 1\newline=−14−1= -14 - 1\newline=−15= -15
  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=−15−(−8)= -15 - (-8)\newline=−15+8= -15 + 8\newline=−7= -7
  5. Write Recursive Formula: Write the recursive formula by plugging in the value of the common difference.\newlineWe can now write the recursive formula by substituting −7-7 for dd in the general recursive formula for an arithmetic sequence, which is an=a(n−1)+da_n = a_{(n - 1)} + d:\newlinean=a(n−1)−7a_n = a_{(n - 1)} - 7

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