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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+38a = -9n + 38\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=−9n+38a = -9n + 38\newlinea = ______
  1. Identify Type: Identify if the given sequence is geometric or arithmetic.\newlineThe explicit formula a=−9n+38a = -9n + 38 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=−9(1)+38a_1 = -9(1) + 38\newlinea1=−9+38a_1 = -9 + 38\newlinea1=29a_1 = 29
  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=−9(2)+38a_2 = -9(2) + 38\newlinea2=−18+38a_2 = -18 + 38\newlinea2=20a_2 = 20
  4. Find Common Difference: Find the common difference in the arithmetic sequence.\newlineThe common difference dd is the difference between consecutive terms:\newlined=a2−a1d = a_2 - a_1\newlined=20−29d = 20 - 29\newlined=−9d = -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. We substitute −9-9 for dd:\newlinean=an−1−9a_n = a_{n - 1} - 9

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