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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–19,–38,–57,–76,…\text{–}19, \text{–}38, \text{–}57, \text{–}76, \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–19,–38,–57,–76,…\text{–}19, \text{–}38, \text{–}57, \text{–}76, \ldots\newlinean=a_n = _____
  1. Identify sequence type: Identify the type of sequence.\newlineWe have: −19-19, −38-38, −57-57, −76-76, ...\newlineIs the given sequence geometric or arithmetic?\newline−19-19, −38-38, −57-57, −76-76, ...\newlineHere, there is a common difference between consecutive terms.\newlineThe given sequence is arithmetic.
  2. Determine values of a1a_1 and dd: Determine the values of a1a_1 and dd of the sequence.\newlineThe first term, a1=−19a_1 = -19\newlineCommon difference, d=−38−(−19)=−19d = -38 - (-19) = -19
  3. Write nth term formula: Write the formula for the nth term of an arithmetic sequence.\newlinean=a1+(n−1)da_n = a_1 + (n-1)d\newlinea1=−19a_1 = -19\newlined=−19d = -19\newlineWrite an expression to describe −19,−38,−57,−76,…-19, -38, -57, -76, \ldots\newlinean=a1+(n−1)da_n = a_1 + (n-1)d\newlinean=−19+(n−1)(−19)a_n = -19 + (n-1)(-19)\newlinean=−19−19n+19a_n = -19 - 19n + 19\newlinean=−19na_n = -19n

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