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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=14n+43a_n = 14n + 43\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=14n+43a_n = 14n + 43\newlinean=_a_n = \_
  1. Find Sequence Terms: First, let's find the first few terms of the sequence by plugging in n=1,2,3,n = 1, 2, 3, and 44 into the explicit formula an=14n+43a_n = 14n + 43.a1=14(1)+43=57a_1 = 14(1) + 43 = 57a2=14(2)+43=71a_2 = 14(2) + 43 = 71a3=14(3)+43=85a_3 = 14(3) + 43 = 85a4=14(4)+43=99a_4 = 14(4) + 43 = 99
  2. Calculate Common Difference: Now, let's find the common difference dd by subtracting consecutive terms.d=a2−a1=71−57=14d = a_2 - a_1 = 71 - 57 = 14d=a3−a2=85−71=14d = a_3 - a_2 = 85 - 71 = 14d=a4−a3=99−85=14d = a_4 - a_3 = 99 - 85 = 14The common difference dd is 1414.
  3. Determine Recursive Formula: Since we have an arithmetic sequence with a common difference of 1414, the recursive formula is an=an−1+da_n = a_{n - 1} + d. Substituting d=14d = 14, we get an=an−1+14a_n = a_{n - 1} + 14.

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