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Write an explicit formula that represents the sequence defined by the following recursive formula: a_(1)=3" and "a_(n)=a_(n-1)+7 Answer: a_(n)=

Write an explicit formula that represents the sequence defined by the following recursive formula:\newlinea1=3 and an=an−1+7 a_{1}=3 \text { and } a_{n}=a_{n-1}+7 \newlineAnswer: an= a_{n}=

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Q. Write an explicit formula that represents the sequence defined by the following recursive formula:\newlinea1=3 and an=an−1+7 a_{1}=3 \text { and } a_{n}=a_{n-1}+7 \newlineAnswer: an= a_{n}=
  1. Identify Terms and Difference: Identify the first term and the common difference from the recursive formula.\newlineThe first term is given as a1=3a_{1}=3. The recursive formula an=an−1+7a_{n}=a_{n-1}+7 indicates that each term is 77 more than the previous term, which means the common difference is 77.
  2. Write Explicit Formula: Use the arithmetic sequence formula to write the explicit formula.\newlineThe general form of an arithmetic sequence is an=a1+(n−1)da_n = a_1 + (n-1)d, where a1a_1 is the first term and dd is the common difference.
  3. Substitute Values: Substitute the values of a1a_{1} and dd into the arithmetic sequence formula.\newlinea1=3a_{1} = 3 and d=7d = 7, so the explicit formula becomes an=3+(n−1)×7a_{n} = 3 + (n-1)\times7.
  4. Simplify Formula: Simplify the explicit formula.\newlinean=3+7n−7a_{n} = 3 + 7n - 7\newlinean=7n−4a_{n} = 7n - 4

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