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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=−15n+34a = -15n + 34\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=−15n+34a = -15n + 34\newlinea=a = ______
  1. Identify Type: Identify if the given sequence is geometric or arithmetic.\newlineThe explicit formula a=−15n+34a = -15n + 34 involves a linear term in nn, which suggests that the sequence is arithmetic, as it does not involve any exponent terms on nn.
  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=−15(1)+34a_1 = -15(1) + 34\newline=−15+34= -15 + 34\newline=19= 19\newlineThis is the first term of the sequence.
  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=−15(2)+34a_2 = -15(2) + 34\newline=−30+34= -30 + 34\newline=4= 4\newlineThis is the second term of the sequence.
  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=4−19= 4 - 19\newline=−15= -15\newlineThis is the common difference of the sequence.
  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 given by an=an−1+da_n = a_{n - 1} + d. We substitute −15-15 for dd to get the recursive formula:\newlinean=an−1−15a_n = a_{n - 1} - 15\newlineThis is the recursive formula for the given sequence.

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