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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+16a = 15n + 16\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+16a = 15n + 16\newlinea=a = ______
  1. Identify Sequence Type: Identify if the given sequence is geometric or arithmetic.\newlineThe sequence defined by a=15n+16a = 15n + 16 involves a linear term in nn without any exponents, which indicates that it is an arithmetic sequence.
  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=15(1)+16a_1 = 15(1) + 16\newlinea1=15+16a_1 = 15 + 16\newlinea1=31a_1 = 31
  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=15(2)+16a_2 = 15(2) + 16\newlinea2=30+16a_2 = 30 + 16\newlinea2=46a_2 = 46
  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\newlined=46−31d = 46 - 31\newlined=15d = 15
  5. Write Recursive Formula: Write the recursive formula by plugging in the value of the common difference.\newlineWe can now write the recursive formula using the common difference dd:\newlinean=a(n−1)+da_n = a_{(n - 1)} + d\newlineSubstituting 1515 for dd, we get:\newlinean=a(n−1)+15a_n = a_{(n - 1)} + 15

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