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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–20,–40,–60,–80,…–20, –40, –60, –80, \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–20,–40,–60,–80,…–20, –40, –60, –80, \ldots\newlinean=a_n = _____
  1. Identify type of sequence: Identify the type of sequence.\newlineThe sequence is −20-20, −40-40, −60-60, −80-80, ...\newlineWe notice that there is a constant difference between consecutive terms, which means the sequence is arithmetic.
  2. Determine first term and common difference: Determine the first term (a1a_1) and the common difference (dd).\newlineThe first term, a1a_1, is −20-20.\newlineThe common difference, dd, can be found by subtracting the first term from the second term: d=−40−(−20)=−20d = -40 - (-20) = -20.
  3. Write formula for nth term: 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=−20a_1 = -20\newlined=−20d = -20\newlineSo, an=−20+(n−1)(−20)a_n = -20 + (n-1)(-20).
  5. Simplify expression: Simplify the expression.\newlinean=−20−20(n−1)a_n = -20 - 20(n-1)\newlinean=−20−20n+20a_n = -20 - 20n + 20\newlinean=−20na_n = -20n

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