A sequence is represented by the formula \( a_{n}=63\left(\frac{1}{3}\right)^{n} \). Starting with \( n=1 \), choose which of the numbers would be included in the first five terms of the sequence.
21
189
\( \frac{7}{27} \)
17
\( \frac{7}{3} \)
\( \frac{7}{19} \)
81

Answer

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Answer

\( a_{5} = 63\left(\frac{1}{3}\right)^{5} = \frac{7}{243} \)

Steps

Step 1 ：\( a_{1} = 63\left(\frac{1}{3}\right)^{1} = 21 \)

Step 2 ：\( a_{2} = 63\left(\frac{1}{3}\right)^{2} = \frac{7}{3} \)

Step 3 ：\( a_{3} = 63\left(\frac{1}{3}\right)^{3} = \frac{7}{27} \)

Step 4 ：\( a_{4} = 63\left(\frac{1}{3}\right)^{4} = \frac{7}{81} \)

Step 5 ：\( a_{5} = 63\left(\frac{1}{3}\right)^{5} = \frac{7}{243} \)