Answer:
a) 2, 1, 0, -3
Explanations:
The given sequence is:
[tex]\begin{gathered} a_n=na_{n-1}-3 \\ \text{where a}_1=2 \end{gathered}[/tex][tex]\begin{gathered} \text{Note that:} \\ n\text{ stands for the number of terms} \\ a_n\text{ stands for the nth term} \end{gathered}[/tex]
For n = 2
[tex]\begin{gathered} a_2=2a_{2-1}-3 \\ a_2=2a_1-3 \\ a_2=\text{ 2(2)-3} \\ a_2=4-3 \\ a_2=1 \end{gathered}[/tex]
For n = 3
[tex]\begin{gathered} a_3=3a_{3-1}-3 \\ a_3=3a_2-3 \\ a_3=3(1)-3 \\ a_3=3-3 \\ a_3=\text{ 0} \end{gathered}[/tex]
For n = 4
[tex]\begin{gathered} a_4=4a_{4-1}-3 \\ a_4=\text{ 4(0)-3} \\ a_4=\text{ 0-3} \\ a_4=\text{ -3} \end{gathered}[/tex][tex]\begin{gathered} a_1=2 \\ a_2=1 \\ a_3=0 \\ a_4=\text{ -3} \end{gathered}[/tex]
The first four terms are 2, 1, 0, -3
