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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. \newline8,16,32,–8, \, –16, \, –32, \, \ldots\newlineWrite your answer using decimals and integers.\newlinean=a_n = ____\_\_\_\_(____)n1\left(\_\_\_\_\right)^{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. \newline8,16,32,–8, \, –16, \, –32, \, \ldots\newlineWrite your answer using decimals and integers.\newlinean=a_n = ____\_\_\_\_(____)n1\left(\_\_\_\_\right)^{n - 1}
  1. Identify sequence type: Identify the type of sequence.\newlineThe sequence is 8-8, 16-16, 32-32, ...\newlineEach term is obtained by multiplying the previous term by a common ratio.\newlineTherefore, 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=8a_1 = -8\newlineTo find the common ratio, divide the second term by the first term: r=(16)/(8)=2r = (-16) / (-8) = 2
  3. Write nth term formula: Write the formula for the nth term of a geometric sequence.\newlineThe formula for the nth term ana_n of a geometric sequence is an=a1r(n1)a_n = a_1 \cdot r^{(n - 1)}.
  4. Substitute values into formula: Substitute the values of a1a_1 and rr into the formula.a1=8a_1 = -8 and r=2r = 2 So, an=(8)×2(n1)a_n = (-8) \times 2^{(n - 1)}

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