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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=−5n+18a = -5n + 18\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=−5n+18a = -5n + 18\newlinea=a = ______
  1. Identify Type: Identify if the given sequence is geometric or arithmetic. The explicit formula a=−5n+18a = -5n + 18 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=−5(1)+18a_1 = -5(1) + 18\newline=−5+18= -5 + 18\newline=13= 13
  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=−5(2)+18a_2 = -5(2) + 18\newline=−10+18= -10 + 18\newline=8= 8
  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=8−13= 8 - 13\newline=−5= -5
  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 −5-5 for dd in the formula:\newlinean=an−1−5a_n = a_{n - 1} - 5

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