Answer:
-2, 8, -12, 28 and -52.
Explanation:
Given the recursively defined sequence:
[tex]\begin{gathered} a_1=-2 \\ a_{n+1}=-2a_n+4 \end{gathered}[/tex]
We want to find the first five terms of the sequence.
The second term:
[tex]\begin{gathered} a_2=a_{1+1}=-2a_1+4 \\ \text{ Substitute }a_1=-2 \\ a_2=-2(-2)+4=4+4 \\ \implies a_2=8 \end{gathered}[/tex]
The third term:
[tex]\begin{gathered} a_3=a_{2+1}=-2a_2+4 \\ \text{ Substitute }a_2=8 \\ a_3=-2(8)+4=-16+4 \\ \implies a_3=-12 \end{gathered}[/tex]
The fourth term:
[tex]\begin{gathered} a_4=a_{3+1}=-2a_3+4 \\ \text{ Substitute }a_3=-12 \\ a_4=-2(-12)+4=24+4 \\ \implies a_4=28 \end{gathered}[/tex]
Finally, we find the fifth term:
[tex]\begin{gathered} a_5=a_{4+1}=-2a_4+4 \\ \text{ Substitute }a_4=28 \\ a_5=-2(28)+4=-56+4 \\ \implies a_5=-52 \end{gathered}[/tex]
The first five terms of the sequence are -2, 8, -12, 28 and -52.
