Question

suppose that a sequence is defined as follows.
$a_1 = -1$, $a_n = -3a_{n - 1} + 6$ for $n \geq 2$
list the first four terms of the sequence.

Explanation:

Step1: Identify first term

$a_1 = -1$

Step2: Calculate second term

Substitute $n=2$, $a_1=-1$ into $a_n=-3a_{n-1}+6$:
$a_2 = -3(-1) + 6 = 3 + 6 = 9$

Step3: Calculate third term

Substitute $n=3$, $a_2=9$ into $a_n=-3a_{n-1}+6$:
$a_3 = -3(9) + 6 = -27 + 6 = -21$

Step4: Calculate fourth term

Substitute $n=4$, $a_3=-21$ into $a_n=-3a_{n-1}+6$:
$a_4 = -3(-21) + 6 = 63 + 6 = 69$

Answer:

$-1$, $9$, $-21$, $69$