Question

suppose that a sequence is defined as follows.
$a_1 = -1$,
$a_n = -4a_{n - 1} + 2$ 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 $n=2$ into recurrence:
$a_2 = -4a_{1} + 2 = -4(-1) + 2 = 4 + 2 = 6$

Step3: Calculate third term

Substitute $n=3$ into recurrence:
$a_3 = -4a_{2} + 2 = -4(6) + 2 = -24 + 2 = -22$

Step4: Calculate fourth term

Substitute $n=4$ into recurrence:
$a_4 = -4a_{3} + 2 = -4(-22) + 2 = 88 + 2 = 90$

Answer:

First four terms: $-1$, $6$, $-22$, $90$