Answer:
Option D. [tex]a_{n}=3an-9a[/tex] is the answer.
Step-by-step explanation:
The given sequence is -6a, -3a, 0a, 3a, 6a...........
Since the given sequence is having a common difference d = -3a - (-6a) = -3a + 6a = 3a
Therefore, the given sequence is an arithmetic sequence.
And for an arithmetic sequence general rule or explicit formula is given by
[tex]T_{n}=a+(n-1)d[/tex]
Where a = first term of the sequence
d = common difference
n = number of term which we have to find
Now we put the values from the given sequence
[tex]T_{n}=-6a+(n-1)3a[/tex]
[tex]T_{n}=-6a+3an-3a[/tex]
[tex]T_{n}=3an-9a[/tex]
Option D. [tex]a_{n}=3an-9a[/tex] is the answer.
