Answer:
To find the first five terms of the sequence defined by \(a_n = 3n^3 - 1\), we substitute \(n = 1, 2, 3, 4, 5\) into the formula and calculate the corresponding values.
1. When \( n = 1 \):
\( a_1 = 3(1)^3 - 1 = 3(1) - 1 = 3 - 1 = 2 \)
2. When \( n = 2 \):
\( a_2 = 3(2)^3 - 1 = 3(8) - 1 = 24 - 1 = 23 \)
3. When \( n = 3 \):
\( a_3 = 3(3)^3 - 1 = 3(27) - 1 = 81 - 1 = 80 \)
4. When \( n = 4 \):
\( a_4 = 3(4)^3 - 1 = 3(64) - 1 = 192 - 1 = 191 \)
5. When \( n = 5 \):
\( a_5 = 3(5)^3 - 1 = 3(125) - 1 = 375 - 1 = 374 \)
Therefore, the first five terms of the sequence \(a_n = 3n^3 - 1\) are:
\( 2, 23, 80, 191, 374 \).
