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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.\newline48,49,50,51,…48, 49, 50, 51, \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.\newline48,49,50,51,…48, 49, 50, 51, \ldots\newlinean=a_n = _____
  1. Sequence Type: We have the sequence: 48,49,50,51,ext...48, 49, 50, 51, ext{...} Is the given sequence geometric or arithmetic? Since there is a constant difference between consecutive terms, the given sequence is arithmetic.
  2. Find a1a_1 and dd: Determine the values of a1a_1 (the first term) and dd (the common difference) of the sequence.\newlineThe first term, a1=48a_1 = 48\newlineCommon difference, d=49−48=1d = 49 - 48 = 1
  3. Arithmetic Sequence Formula: Use the formula for the nth term of an arithmetic sequence: \newlinean=a1+(n−1)da_n = a_1 + (n-1)d\newlineSubstitute the values of a1a_1 and dd into the formula.\newlinea1=48a_1 = 48\newlined=1d = 1\newlinean=48+(n−1)×1a_n = 48 + (n-1) \times 1
  4. Simplify Expression: Simplify the expression:\newlinean=48+n−1a_{n} = 48 + n - 1\newlinean=n+47a_{n} = n + 47

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