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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-68,-136,-204,-272,\text{-}68, \text{-}136, \text{-}204, \text{-}272, \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-68,-136,-204,-272,\text{-}68, \text{-}136, \text{-}204, \text{-}272, \ldots\newlinean=a_n = _____
  1. Identify sequence type: Identify the type of sequence.\newlineWe have: \newline68,136,204,272,–68, –136, –204, –272, \dots\newlineIs the given sequence geometric or arithmetic? \newlineSince there is a common difference between consecutive terms, the given sequence is arithmetic.
  2. Find first term and difference: Determine the first term (a1a_1) and the common difference (dd) of the sequence.\newlineThe first term, a1=68a_1 = -68\newlineCommon difference, d=136(68)=68d = -136 - (-68) = -68
  3. Write nth term formula: Write the formula for the nth term of an arithmetic sequence. an=a1+(n1)da_n = a_1 + (n-1)d
  4. Substitute values into formula: Substitute the values of a1a_1 and dd into the formula.\newlinea1=68a_1 = -68\newlined=68d = -68\newlinean=68+(n1)(68)a_n = -68 + (n-1)(-68)
  5. Simplify expression: Simplify the expression.\newlinean=6868(n1)a_n = -68 - 68(n-1)\newlinean=6868n+68a_n = -68 - 68n + 68\newlinean=68na_n = -68n

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