Question

find the first 5 terms.\

$$\begin{cases}a_0 = 1\\\\a_n = -2a_{n - 1}\\end{cases}$$

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$$\begin{tabular}{|c|c|c|c|c|}\\hline$a_0$ & $a_1$ & $a_2$ & $a_3$ & $a_4$\\\\\\hline? & & & & \\\\\\hline\\end{tabular}$$

Explanation:

Step1: Identify \( a_0 \)

Given \( a_0 = 1 \).

Step2: Calculate \( a_1 \)

Using the recurrence relation \( a_n=-2a_{n - 1} \), for \( n = 1 \):
\( a_1=-2a_{0}=-2\times1=-2 \)

Step3: Calculate \( a_2 \)

For \( n = 2 \):
\( a_2=-2a_{1}=-2\times(-2)=4 \)

Step4: Calculate \( a_3 \)

For \( n = 3 \):
\( a_3=-2a_{2}=-2\times4=-8 \)

Step5: Calculate \( a_4 \)

For \( n = 4 \):
\( a_4=-2a_{3}=-2\times(-8)=16 \)

Answer:

\( a_0 = 1 \), \( a_1 = -2 \), \( a_2 = 4 \), \( a_3 = -8 \), \( a_4 = 16 \)