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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=−16n+11a = -16n + 11\newlinea = ______

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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=−16n+11a = -16n + 11\newlinea = ______
  1. Identify Sequence Type: Identify if the given sequence is geometric or arithmetic.\newlineThe explicit formula a=−16n+11a = -16n + 11 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, substitute n=1n = 1 into the explicit formula:\newlinea1=−16(1)+11a_1 = -16(1) + 11\newlinea1=−16+11a_1 = -16 + 11\newlinea1=−5a_1 = -5
  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=−16(2)+11a_2 = -16(2) + 11\newlinea2=−32+11a_2 = -32 + 11\newlinea2=−21a_2 = -21
  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\newlined=−21−(−5)d = -21 - (-5)\newlined=−21+5d = -21 + 5\newlined=−16d = -16
  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 −16-16 for dd:\newlinean=an−1−16a_n = a_{n - 1} - 16

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