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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=−4n+3a = -4n + 3\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=−4n+3a = -4n + 3\newlinea = ______
  1. Identify Sequence Type: Identify if the given sequence is geometric or arithmetic.\newlineThe explicit formula a=−4n+3a = -4n + 3 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=−4(1)+3a_1 = -4(1) + 3\newline=−4+3= -4 + 3\newline=−1= -1
  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=−4(2)+3a_2 = -4(2) + 3\newline=−8+3= -8 + 3\newline=−5= -5
  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=−5−(−1)= -5 - (-1)\newline=−5+1= -5 + 1\newline=−4= -4
  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 −4-4 for dd in the formula:\newlinean=an−1−4a_n = a_{n - 1} - 4

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