Answer:
-4, 14, -22 and 50.
Explanation:
Given the sequence defined as follows:
[tex]\begin{gathered} a_1=-4 \\ a_n=-2a_{n-1}+6 \end{gathered}[/tex][tex]\begin{gathered} \text{The second term:} \\ a_2=-2a_{2-1}+6 \\ =-2a_1+6 \\ =-2(-4)+6 \\ =8+6 \\ a_2=14 \end{gathered}[/tex]Similarly:
[tex]\begin{gathered} \text{The third term:} \\ a_3=-2a_{3-1}+6 \\ =-2a_2+6 \\ =-2(14)+6 \\ =-28+6 \\ a_3=-22 \end{gathered}[/tex]Finally, the fourth term:
[tex]\begin{gathered} a_4=-2a_{4-1}+6 \\ =-2a_3+6 \\ =-2\mleft(-22\mright)+6 \\ =44+6 \\ a_4=50 \end{gathered}[/tex]Therefore, the first four terms of the sequence are -4, 14, -22, and 50.
