Answer:
The answer is [tex]a_n=6a-3a(n-1)[/tex]
Step-by-step explanation:
In order to determine the general rule, we have to identify the difference between each term. We have to subtract every two continuous terms:
[tex]3a-6a=-3a\\0-3a=-3a\\-3a-0=-3a\\-6a-(-3a)=-6a+3a=-3a[/tex]
Then, we know that we have to subtract -3a to every next term. The first term of the sequence is 6a and after that we have to subtract -3a since the second to the nth term.
Thus the nth term of the sequence is:
[tex]a_n=6a-3a(n-1)[/tex]
To check the expression:
[tex]n=1\\a_1=6a-3a(1-1)=6a-3a(0)=6a\\\\n=3\\a_3=6a-3a(3-1)=6a-3a(2)=6a-6a=0[/tex]
So, the expression is right.
