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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–78,–77,–76,–75,…–78, –77, –76, –75, \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–78,–77,–76,–75,…–78, –77, –76, –75, \ldots\newlinean=a_n = _____
  1. Identify Sequence Type: We have: \newline–7878, –7777, –7676, –7575, ... \newlineIs the given sequence geometric or arithmetic? \newline–7878, –7777, –7676, –7575, ... \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=−78a_1 = -78 \newlineCommon difference, d=−77−(−78)=1d = -77 - (-78) = 1
  3. Calculate an: We have: \newlinean=a1+(n−1)da_n = a_1 + (n-1)d \newlinea1=−78a_1 = -78 \newlined=1d = 1 \newlineWrite an expression to describe −78,−77,−76,−75,...-78, -77, -76, -75, ... \newlinean=a1+(n−1)da_n = a_1 + (n-1)d \newlinean=−78+(n−1)×1a_n = -78 + (n-1) \times 1 \newlinean=−78+n−1a_n = -78 + n - 1 \newlinean=n−79a_n = n - 79

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