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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–89,–178,–267,–356,…–89, –178, –267, –356, \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–89,–178,–267,–356,…–89, –178, –267, –356, \ldots\newlinean=a_n = _____
  1. Sequence Type: We have: \newline–8989, –178178, –267267, –356356, ... \newlineIs the given sequence geometric or arithmetic? \newline–8989, –178178, –267267, –356356, ... \newlineHere, there is a common difference between consecutive terms.\newlineThe given sequence is arithmetic.
  2. Find a1a_1 and dd: Determine the values of a1a_1 and dd of the sequence. \newlineThe first term, a1=−89a_1 = -89 \newlineCommon difference, d=−178−(−89)=−89d = -178 - (-89) = -89
  3. Expression for an: We have: \newlinean=a1+(n−1)da_n = a_1 + (n-1)d \newlinea1=−89a_1 = -89 \newlined=−89d = -89 \newlineWrite an expression to describe −89,−178,−267,−356,…-89, -178, -267, -356, \ldots \newlinean=a1+(n−1)da_n = a_1 + (n-1)d \newlinean=−89+(n−1)×(−89)a_n = -89 + (n-1) \times (-89) \newlinean=−89−89n+89a_n = -89 - 89n + 89 \newlinean=−89na_n = -89n

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