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Use the explicit formula to find a recursive formula for the sequence ana_n. Write your answer in simplest form.\newlineThe recursive formula should depend on an−1a_{n - 1}.\newlinean=3n+37a_n = 3n + 37\newlinean=_a_n = \_

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Q. Use the explicit formula to find a recursive formula for the sequence ana_n. Write your answer in simplest form.\newlineThe recursive formula should depend on an−1a_{n - 1}.\newlinean=3n+37a_n = 3n + 37\newlinean=_a_n = \_
  1. Find First Term: Let's plug in n=1n = 1 to find the first term, a1=3(1)+37=40a_1 = 3(1) + 37 = 40.
  2. Find Second Term: Now, plug in n=2n = 2 to find the second term, a2=3(2)+37=43a_2 = 3(2) + 37 = 43.
  3. Calculate Common Difference: Notice that a2−a1=43−40=3a_2 - a_1 = 43 - 40 = 3, which is the common difference dd.
  4. Arithmetic Sequence Recursive Formula: The recursive formula for an arithmetic sequence is an=an−1+da_n = a_{n - 1} + d. Here, d=3d = 3.
  5. Final Recursive Formula: So, the recursive formula is an=an−1+3a_n = a_{n - 1} + 3.

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