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

the answer in this case would be an = 3an + 9a

Answer 2

a(n) = -9a + 3an

Explanation:

The first term is -6a and the next term is found by adding 3a to it. Thus, this is an arithmetic sequence with common difference 3a.

The general arithmetic sequence formula is a(n) = a(1) + (n - 1)d, where d is the common difference. Here d = 3a.

So the general rule for the given sequence is:

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

But this can be simplified. Perform the indicated multiplication, obtaining:

a(n) = -6a - 3a + 3an, or

a(n) = -9a + 3an