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Write an explicit formula for a_(n), the n^("th ") term of the sequence 5,7,9,dots Answer: a_(n)=

Write an explicit formula for an a_{n} , the nth  n^{\text {th }} term of the sequence 5,7,9,… 5,7,9, \ldots \newlineAnswer: an= a_{n}=

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Q. Write an explicit formula for an a_{n} , the nth  n^{\text {th }} term of the sequence 5,7,9,… 5,7,9, \ldots \newlineAnswer: an= a_{n}=
  1. Identify Sequence Type: Identify whether the given sequence is geometric or arithmetic. The sequence 5,7,9,…5, 7, 9, \ldots has a common difference between consecutive terms, so it is an arithmetic sequence.
  2. Use Explicit Formula: Use the explicit formula for an arithmetic sequence, an=a1+(n−1)da_n = a_1 + (n-1)d, where a1a_1 is the first term and dd is the common difference. For the sequence 5,7,9,…5, 7, 9, \ldots, the first term, a1a_1, is 55 and the common difference, dd, is 22.
  3. Substitute Values: Substitute the values of a1a_1 and dd into the formula to write an expression to describe the sequence. The expression for the sequence 5,7,9,…5, 7, 9, \ldots is an=5+(n−1)×2a_n = 5 + (n-1) \times 2.
  4. Simplify Expression: Simplify the expression. an=5+2n−2a_n = 5 + 2n - 2, which simplifies to an=2n+3a_n = 2n + 3.

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