Question

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

-6a, -3a, 0a, 3a, 6a. . .

an = 3an + 9a
an = -3an - 9a
an = -3an + 9a
an = 3an - 9a

Answer 1

difference=3a

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

=3an-9a

Answer 2

Option D.
`a_(n)=3an-9a` is the answer.

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.