To find the first five terms of the recursive sequence \(a_n = 3a_{n-1} - 6\) with the initial value \(a_1 = 7\), you can use the recursive formula to generate each term
1. \(a_1 = 7\) (given)
2. \(a_2 = 3a_1 - 6 = 3(7) - 6 = 21 - 6 = 15\)
3. \(a_3 = 3a_2 - 6 = 3(15) - 6 = 45 - 6 = 39\)
4. \(a_4 = 3a_3 - 6 = 3(39) - 6 = 117 - 6 = 111\)
5. \(a_5 = 3a_4 - 6 = 3(111) - 6 = 333 - 6 = 327\)
So, the first five terms of the sequence are:
\(a_1 = 7\)
\(a_2 = 15\)
\(a_3 = 39\)
\(a_4 = 111\)
\(a_5 = 327\)