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Write an expression to describe the sequence below. Use nn to represent the position of a term in the sequence, where n=1n = 1 for the first term.\newline–13,–26,–39,–52,…–13, –26, –39, –52, \ldots\newlinean=a_n = _____

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Q. Write an expression to describe the sequence below. Use nn to represent the position of a term in the sequence, where n=1n = 1 for the first term.\newline–13,–26,–39,–52,…–13, –26, –39, –52, \ldots\newlinean=a_n = _____
  1. Identify type of sequence: Identify the type of sequence.\newlineWe have: \newline–13–13, –26–26, –39–39, –52–52, ...\newlineIs the given sequence geometric or arithmetic? \newlineSince there is a common difference between consecutive terms, the given sequence is arithmetic.
  2. Determine first term and difference: Determine the first term (a1a_1) and the common difference (dd) of the sequence.\newlineThe first term, a1=−13a_1 = -13\newlineCommon difference, d=−26−(−13)=−13d = -26 - (-13) = -13
  3. Write formula for nth term: Write the formula for the nth term of an arithmetic sequence. an=a1+(n−1)da_n = a_1 + (n-1)d
  4. Substitute values into formula: Substitute the values of a1a_1 and dd into the formula.a1=−13a_1 = -13d=−13d = -13an=−13+(n−1)(−13)a_n = -13 + (n-1)(-13)
  5. Simplify expression: Simplify the expression.\newlinean=−13−13(n−1)a_n = -13 - 13(n-1)\newlinean=−13−13n+13a_n = -13 - 13n + 13\newlinean=−13na_n = -13n

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