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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=−17n−20a = -17n - 20\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=−17n−20a = -17n - 20\newlinea=a = ______
  1. Identify Type: Identify if the given sequence is geometric or arithmetic.\newlineThe explicit formula a=−17n−20a = -17n - 20 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=−17(1)−20a_1 = -17(1) - 20\newlinea1=−17−20a_1 = -17 - 20\newlinea1=−37a_1 = -37
  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=−17(2)−20a_2 = -17(2) - 20\newlinea2=−34−20a_2 = -34 - 20\newlinea2=−54a_2 = -54
  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=−54−(−37)d = -54 - (-37)\newlined=−54+37d = -54 + 37\newlined=−17d = -17
  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 −17-17 for dd in the formula:\newlinean=an−1−17a_n = a_{n - 1} - 17

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