Question

Indicate a general rule for the nth term of this sequence.

Answer 1

difference=3a

so an=-6a+(n-1)3a

=3an-9a

Answer 2

Answer:

Option D. $a_{n}=3an-9a$ 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

$T_{n}=a+(n-1)d$

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

$T_{n}=-6a+(n-1)3a$

$T_{n}=-6a+3an-3a$

$T_{n}=3an-9a$

Option D. $a_{n}=3an-9a$ is the answer.