Question

suppose that a sequence is defined as follows.
$a_1 = 5$, $a_n = -4a_{n - 1} + 10$ for $n \geq 2$
list the first four terms of the sequence.

Explanation:

Step1: Identify first term

$a_1 = 5$

Step2: Calculate second term

Substitute $n=2$, $a_1=5$ into formula:
$a_2 = -4a_1 + 10 = -4(5) + 10 = -20 + 10 = -10$

Step3: Calculate third term

Substitute $n=3$, $a_2=-10$ into formula:
$a_3 = -4a_2 + 10 = -4(-10) + 10 = 40 + 10 = 50$

Step4: Calculate fourth term

Substitute $n=4$, $a_3=50$ into formula:
$a_4 = -4a_3 + 10 = -4(50) + 10 = -200 + 10 = -190$

Answer:

5, -10, 50, -190