Schneider Burns
08/30/2023 · Senior High School
Generate the first 3 terms of the sequence defined by \( a_{n}=\frac{2}{3 n} \)
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Step-by-step Solution
To find the first three terms of the sequence defined by \( a_n = \frac{2}{3n} \), we will substitute \( n = 1, 2, \) and \( 3 \) into the formula.
1. For \( n = 1 \):
\[
a_1 = \frac{2}{3 \cdot 1} = \frac{2}{3}
\]
2. For \( n = 2 \):
\[
a_2 = \frac{2}{3 \cdot 2} = \frac{2}{6} = \frac{1}{3}
\]
3. For \( n = 3 \):
\[
a_3 = \frac{2}{3 \cdot 3} = \frac{2}{9}
\]
Thus, the first three terms of the sequence are:
\[
\frac{2}{3}, \frac{1}{3}, \frac{2}{9}
\]
Quick Answer
The first three terms are \( \frac{2}{3}, \frac{1}{3}, \frac{2}{9} \).
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