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Write an equation to describe the sequence below. Use n n to represent the position of a term in the sequence, where n=1 n = 1 for the first term.\newline9,18,36,… 9 , 18 , 36 , \ldots \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 n n to represent the position of a term in the sequence, where n=1 n = 1 for the first term.\newline9,18,36,… 9 , 18 , 36 , \ldots \newlineWrite your answer using decimals and integers.\newlinean= a_n = _____(_____)n−1^{n - 1}
  1. Identify sequence type: Identify the type of sequence.\newlineThe sequence is 9,18,36,…9, 18, 36, \ldots where each term appears to be twice the previous term. This suggests that the sequence is geometric.
  2. Determine first term and ratio: Determine the first term (a1a_1) and the common ratio (rr).\newlineThe first term a1a_1 is the first number in the sequence, which is 99.\newlineTo find the common ratio rr, we divide the second term by the first term: r=189=2r = \frac{18}{9} = 2.
  3. Write nth term formula: Write the formula for the nth term of a geometric sequence.\newlineThe nth term ana_n of a geometric sequence is given by the formula an=a1⋅r(n−1)a_n = a_1 \cdot r^{(n - 1)}.
  4. Substitute values into formula: Substitute the values of a1a_1 and rr into the formula.\newlineWe have a1=9a_1 = 9 and r=2r = 2, so the formula becomes an=9×2(n−1)a_n = 9 \times 2^{(n - 1)}.

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