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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.\newline31,30,29,28,–31, –30, –29, –28, \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.\newline31,30,29,28,–31, –30, –29, –28, \ldots\newlinean=a_n = _____
  1. Identify type of sequence: Identify the type of sequence.\newlineThe sequence is 31-31, 30-30, 29-29, 28-28, .... We need to determine if this sequence is arithmetic or geometric. By looking at the sequence, we can see that there is a constant difference between consecutive terms, which means the sequence is arithmetic.
  2. Find first term and difference: Find the first term and the common difference.\newlineThe first term of the sequence, a1a_{1}, is 31–31. To find the common difference, dd, we subtract the first term from the second term: d=(30)(31)=30+31=1d = (–30) – (–31) = –30 + 31 = 1.
  3. Write formula for nth term: Write the formula for the nth term of an arithmetic sequence. The general formula for the nth term of an arithmetic sequence is an=a1+(n1)da_n = a_1 + (n-1)d. We have a1=31a_1 = -31 and d=1d = 1.
  4. Substitute values into formula: Substitute the values of a1a_{1} and dd into the formula.\newlineSubstituting the values into the formula gives us an=(31)+(n1)(1)a_{n} = (-31) + (n-1)(1).
  5. Simplify the expression: Simplify the expression.\newlineSimplifying the expression, we get an=31+n1a_n = -31 + n - 1. Combining like terms, we get an=n32a_n = n - 32.

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