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Write an explicit formula for a_(n), the n^("th ") term of the sequence 27,23,19,dots Answer: a_(n)=

Write an explicit formula for an a_{n} , the nth  n^{\text {th }} term of the sequence 27,23,19,… 27,23,19, \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 27,23,19,… 27,23,19, \ldots \newlineAnswer: an= a_{n}=
  1. Identify Terms: To find the explicit formula for the nnth term of an arithmetic sequence, we need to identify the first term (a1a_1) and the common difference (dd).
  2. First Term and Difference: The first term of the sequence is 2727. This is given directly by the sequence.
  3. Calculate Common Difference: To find the common difference, we subtract the second term from the first term: 23−27=−423 - 27 = -4. The common difference is −4-4.
  4. Use Explicit Formula: The explicit formula for an arithmetic sequence is given by an=a1+(n−1)da_n = a_1 + (n - 1)d. We will use this formula with our identified values for a1a_1 and dd.
  5. Substitute Values: Substitute the values into the formula: an=27+(n−1)(−4)a_n = 27 + (n - 1)(-4).
  6. Simplify Formula: Simplify the formula: an=27−4n+4a_n = 27 - 4n + 4.
  7. Combine Like Terms: Combine like terms: an=31−4na_n = 31 - 4n.

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