Question

suppose that a sequence is defined as follows.
$a_1 = -2$, $a_n = 4a_{n - 1} + 5$ for $n \geq 2$
list the first four terms of the sequence.
$\square, \square, \square, \square$

Explanation:

Step1: Identify first term

$a_1 = -2$

Step2: Calculate second term

Substitute $n=2$, $a_1=-2$ into $a_n=4a_{n-1}+5$:
$a_2 = 4(-2) + 5 = -8 + 5 = -3$

Step3: Calculate third term

Substitute $n=3$, $a_2=-3$ into $a_n=4a_{n-1}+5$:
$a_3 = 4(-3) + 5 = -12 + 5 = -7$

Step4: Calculate fourth term

Substitute $n=4$, $a_3=-7$ into $a_n=4a_{n-1}+5$:
$a_4 = 4(-7) + 5 = -28 + 5 = -23$

Answer:

$-2, -3, -7, -23$