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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-95,-94,-93,-92,…\text{-}95, \text{-}94, \text{-}93, \text{-}92, \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-95,-94,-93,-92,…\text{-}95, \text{-}94, \text{-}93, \text{-}92, \ldots\newlinean=a_n = _____
  1. Identify Sequence Type: Identify the type of sequence.\newlineThe sequence is −95-95, −94-94, −93-93, −92-92, ...\newlineWe notice that there is a common difference between consecutive terms, which means the sequence is arithmetic.
  2. Determine First Term and Difference: Determine the first term (a1a_1) and the common difference (dd).\newlineThe first term, a1a_1, is −95-95.\newlineThe common difference, dd, is the difference between the second term and the first term: d=−94−(−95)=−94+95=1d = -94 - (-95) = -94 + 95 = 1.
  3. Write Formula for nth Term: Write the formula for the nth term of an arithmetic sequence.\newlineThe nth term of an arithmetic sequence is given by: an=a1+(n−1)da_n = a_1 + (n-1)d.
  4. Substitute Values into Formula: Substitute the values of a1a_{1} and dd into the formula.a1=−95a_{1} = -95d=1d = 1So, an=−95+(n−1)×1a_{n} = -95 + (n-1)\times 1
  5. Simplify Expression: Simplify the expression.\newlinean=−95+n−1a_n = -95 + n - 1\newlinean=n−96a_n = n - 96

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