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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=13n−27a = 13n - 27\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=13n−27a = 13n - 27\newlinea=a = ______
  1. Identify Sequence Type: Identify if the given sequence is geometric or arithmetic.\newlineThe sequence defined by a=13n−27a = 13n - 27 involves a linear term in nn and does not involve any exponent terms. Hence, the given sequence is arithmetic.
  2. Find First Term: Find the first term of the sequence using the explicit formula.\newlineTo find the first term a1a_1, we substitute n=1n = 1 into the explicit formula:\newlinea1=13(1)−27a_1 = 13(1) - 27\newlinea1=13−27a_1 = 13 - 27\newlinea1=−14a_1 = -14
  3. Find Second Term: Find the second term of the sequence using the explicit formula.\newlineTo find the second term a2a_2, we substitute n=2n = 2 into the explicit formula:\newlinea2=13(2)−27a_2 = 13(2) - 27\newlinea2=26−27a_2 = 26 - 27\newlinea2=−1a_2 = -1
  4. Find Common Difference: Find the common difference in the arithmetic sequence.\newlineThe common difference dd is the difference between any two consecutive terms. We can calculate it as:\newlined=a2−a1d = a_2 - a_1\newlined=−1−(−14)d = -1 - (-14)\newlined=−1+14d = -1 + 14\newlined=13d = 13
  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 1313 for dd to get:\newlinean=an−1+13a_n = a_{n - 1} + 13\newlineThis is the recursive formula for the given sequence.

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