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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.\newline24,25,26,27,…24, 25, 26, 27, \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.\newline24,25,26,27,…24, 25, 26, 27, \ldots\newlinean=a_n = _____
  1. Identify type of sequence: Identify the type of sequence.\newlineThe sequence is 24,25,26,27,…24, 25, 26, 27, \ldots Each term increases by 11 from the previous term, which indicates that this is an arithmetic sequence.
  2. Determine first term and difference: Determine the first term (a1a_1) and the common difference (dd).\newlineThe first term a1a_1 is 2424.\newlineTo find the common difference dd, subtract the first term from the second term: d=25−24=1d = 25 - 24 = 1.
  3. Write formula for nth term: Write the formula for the nth term of an arithmetic sequence.\newlineThe nth term ana_n of an arithmetic sequence is given by the formula: 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=24a_{1} = 24 and d=1d = 1, so the expression for the nth term is:an=24+(n−1)×1a_{n} = 24 + (n - 1)\times1.
  5. Simplify expression: Simplify the expression. an=24+n−1a_{n} = 24 + n - 1. an=n+23a_{n} = n + 23.

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