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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–7,–14,–21,–28,...–7, –14, –21, –28, ...\newline_____

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Write variable expressions for arithmetic sequencesright chevron icon

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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–7,–14,–21,–28,...–7, –14, –21, –28, ...\newline_____
  1. Find Common Difference: Look at the difference between the terms to find the common difference. \newline−14−(-7)=-7-14 - (\text{-}7) = \text{-}7, −21−(-14)=-7-21 - (\text{-}14) = \text{-}7, and so on.\newlineThe common difference is −7-7.
  2. General Form of Sequence: Write the general form of an arithmetic sequence: an=a1+(n−1)da_n = a_1 + (n - 1)d, where ana_n is the nnth term, a1a_1 is the first term, nn is the term number, and dd is the common difference.
  3. Plug in Values: Plug in the values from the sequence: a1=−7a_1 = -7 and d=−7d = -7. an=−7+(n−1)(−7)a_n = -7 + (n - 1)(-7).
  4. Simplify Expression: Simplify the expression. an=−7−7n+7a_n = -7 - 7n + 7. Oops, there's a mistake here. The correct simplification should be an=−7+(–7)(n−1)=−7−7n+7a_n = -7 + (–7)(n - 1) = -7 - 7n + 7.

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