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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.\newline80,81,82,83,…80, 81, 82, 83, \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.\newline80,81,82,83,…80, 81, 82, 83, \ldots\newlinean=a_n = _____
  1. Identify sequence type: Identify the type of sequence.\newlineThe sequence is 80,81,82,83,…80, 81, 82, 83, \ldots\newlineWe notice that there is a constant 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) of the sequence.\newlineThe first term, a1a_1, is 8080.\newlineThe common difference, dd, is the difference between any two consecutive terms, which is 81−80=181 - 80 = 1.
  3. Write general nth term formula: Write the general formula for the nth term of an arithmetic sequence.\newlineThe nth term of an arithmetic sequence is given by the formula:\newlinean=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=80a_{1} = 80d=1d = 1So, the expression for the nth term is:an=80+(n−1)×1a_{n} = 80 + (n-1)\times1
  5. Simplify nth term expression: Simplify the expression for the nth term.\newlinean=80+n−1a_n = 80 + n - 1\newlinean=n+79a_n = n + 79

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