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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.\newline55,56,57,58,…55, 56, 57, 58, \dots\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.\newline55,56,57,58,…55, 56, 57, 58, \dots\newlinean=a_n = _____
  1. Sequence Type: We have the sequence: 55,56,57,58,…55, 56, 57, 58, \ldots\newlineIs the given sequence geometric or arithmetic?\newline55,56,57,58,…55, 56, 57, 58, \ldots\newlineHere, there is a common difference between consecutive terms.\newlineThe given sequence is arithmetic.
  2. Determine Values: Determine the values of a1a_1 and dd of the sequence.\newlineThe first term, a1=55a_1 = 55\newlineCommon difference, d=56−55=1d = 56 - 55 = 1
  3. Arithmetic Sequence Formula: We have the formula for the nnth term of an arithmetic sequence:\newlinean=a1+(n−1)da_n = a_1 + (n-1)d\newlinea1=55a_1 = 55\newlined=1d = 1\newlineWrite an expression to describe 5555, 5656, 5757, 5858, ...\newlinean=a1+(n−1)da_n = a_1 + (n-1)d\newlinean=55+(n−1)×1a_n = 55 + (n-1) \times 1\newlinean=55+n−1a_n = 55 + n - 1\newlinean=n+54a_n = n + 54

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