Question

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

Explanation:

Step1: Identify the first term

The first term \( a_1 \) is given as \( 2 \).

Step2: Calculate the second term (\(n = 2\))

Using the formula \( a_n=-3a_{n - 1} \) with \( n = 2 \) and \( a_1 = 2 \), we get \( a_2=-3\times a_1=-3\times2=-6 \).

Step3: Calculate the third term (\(n = 3\))

Using the formula with \( n = 3 \) and \( a_2=-6 \), we get \( a_3=-3\times a_2=-3\times(-6)=18 \).

Step4: Calculate the fourth term (\(n = 4\))

Using the formula with \( n = 4 \) and \( a_3=18 \), we get \( a_4=-3\times a_3=-3\times18=-54 \).

Answer:

\( 2 \), \( -6 \), \( 18 \), \( -54 \)