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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–36,–72,–108,–144,…\text{–}36, \text{–}72, \text{–}108, \text{–}144, \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–36,–72,–108,–144,…\text{–}36, \text{–}72, \text{–}108, \text{–}144, \ldots\newlinean=a_n = _____
  1. Identify type of sequence: Identify the type of sequence.\newlineWe have: −36-36, −72-72, −108-108, −144-144, ...\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 common difference: Determine the first term (a1a_1) and the common difference (dd) of the sequence.\newlineThe first term, a1=−36a_1 = -36\newlineCommon difference, d=−72−(−36)=−36d = -72 - (-36) = -36
  3. Write formula for nth term: Write the formula for the nth term of an arithmetic sequence.\newlinean=a1+(n−1)da_n = a_1 + (n-1)d\newlineSubstitute the values of a1a_1 and dd into the formula.\newlinea1=−36a_1 = -36\newlined=−36d = -36\newlinean=−36+(n−1)(−36)a_n = -36 + (n-1)(-36)
  4. Simplify the expression: Simplify the expression.\newlinean=−36−36(n−1)a_{n} = -36 - 36(n-1)\newlinean=−36−36n+36a_{n} = -36 - 36n + 36\newlinean=−36na_{n} = -36n

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