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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.\newline31,32,33,34,…31, 32, 33, 34, \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.\newline31,32,33,34,…31, 32, 33, 34, \ldots\newlinean=a_n = _____
  1. Identify sequence type: Identify the type of sequence.\newlineThe sequence is 31,32,33,34,…31, 32, 33, 34, \ldots\newlineWe notice that there is a constant difference between consecutive terms, which means the sequence is arithmetic.
  2. Find first term and difference: Determine the first term (a1a_1) and the common difference (dd). The first term, a1a_1, is 3131. To find the common difference, we subtract the first term from the second term: d=32−31=1d = 32 - 31 = 1.
  3. Write nth term formula: Write the formula for the nth term of an arithmetic sequence.\newlineThe nth term 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.\newlinea1=31a_1 = 31 and d=1d = 1.\newlineSo, an=31+(n−1)×1a_n = 31 + (n-1)\times1.
  5. Simplify expression: Simplify the expression.\newlinean=31+n−1a_n = 31 + n - 1.\newlinean=n+30a_n = n + 30.

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