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Write an equation 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. \newline6, −18, 54, …6, \, -18, \, 54, \, \dots\newlineWrite your answer using decimals and integers.\newlinean=a_n = ____\_\_\_\_(____\_\_\_\_)n−1^{n - 1}

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Q. Write an equation 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. \newline6, −18, 54, …6, \, -18, \, 54, \, \dots\newlineWrite your answer using decimals and integers.\newlinean=a_n = ____\_\_\_\_(____\_\_\_\_)n−1^{n - 1}
  1. Identify sequence type: Identify the type of sequence.\newlineWe have the sequence: 6,−18,54,…6, -18, 54, \ldots\newlineTo determine if the sequence is arithmetic or geometric, we look at the relationship between consecutive terms.\newline66 to −18-18 is multiplied by −3-3, and −18-18 to 5454 is also multiplied by −3-3.\newlineSince each term is multiplied by a common ratio, the sequence is geometric.
  2. Determine first term and ratio: Determine the first term (a1a_1) and the common ratio (rr).\newlineThe first term: a1=6a_1 = 6\newlineTo find the common ratio, divide the second term by the first term: r=−186=−3r = \frac{-18}{6} = -3
  3. Write nth term formula: Write the formula for the nth term of a geometric sequence.\newlineThe general formula for the nth term of a geometric sequence is:\newlinean=a1×r(n−1)a_{n} = a_{1} \times r^{(n - 1)}
  4. Substitute values into formula: Substitute the values of a1a_1 and rr into the formula.\newlineSubstitute 66 for a1a_1 and −3-3 for rr into the formula:\newlinean=6×(−3)n−1a_n = 6 \times (-3)^{n - 1}

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