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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.\newline−40,−80,−120,−160,…-40, -80, -120, -160, \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.\newline−40,−80,−120,−160,…-40, -80, -120, -160, \ldots\newlinean=a_n = _____
  1. Identify type of sequence: Identify the type of sequence.\newlineThe sequence is −40-40, −80-80, −120-120, −160-160, ... \newlineWe need to determine if this sequence is arithmetic or geometric. By observing the differences between consecutive terms, we can see that each term is decreasing by the same amount.
  2. Find first term and difference: Find the first term and the common difference.\newlineThe first term, a1a_1, is −40-40.\newlineTo find the common difference, dd, we subtract the first term from the second term: d=−80−(−40)=−40d = -80 - (-40) = -40.
  3. Write formula for nth term: Write the formula for the nth term of an arithmetic sequence.\newlineThe general formula for the nth term of an arithmetic sequence is:\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=−40a_1 = -40d=−40d = -40Now, we substitute these values into the formula:an=−40+(n−1)(−40)a_n = -40 + (n-1)(-40)
  5. Simplify expression: Simplify the expression.\newlinean=−40−40(n−1)a_{n} = -40 - 40(n-1)\newlinean=−40−40n+40a_{n} = -40 - 40n + 40\newlinean=−40na_{n} = -40n

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