Answer :
Sequences
We know that
[tex]\begin{gathered} a_1_{}^{}=6 \\ a_n=a_{n-1}-4 \end{gathered}[/tex]We want to find a₄, in order to find it we have to find the previous terms:
a₁, a₂, a₃
In order to find a₂ we use the previous term a₁:
[tex]\begin{gathered} a_1=6 \\ a_2=a_{2-1}-4 \\ =a_1-4 \\ =6-4=2_{} \end{gathered}[/tex]Similarly, we find a₃
[tex]\begin{gathered} a_2=2 \\ a_3=a_{3-1}-4 \\ =a_2-4 \\ =2-4=-2 \end{gathered}[/tex]Now we can find a₄, using a₃:
[tex]\begin{gathered} a_3=-2 \\ a_4=a_{4-1}-4 \\ =a_3-4 \\ =-2-4=-6 \end{gathered}[/tex]