Question

What is the general rule for the arithmetic sequence?

15, 12, 9, 6, …
A.
3n – 18
B.
6(3 – n)
C.
3n + 12
D.
18 – 3n

Answer 1

Try each one for a few terms, and see which one works.

Answer 2

-3

Answer 3

15, 12, 9, 6, …
What is the common difference d?

Answer 4

you subtract 3 so its -3

Answer 5

B

Answer 6

Once you find d, the nth term of an arithmetic sequence is:
\(\Large a_n = a_1 + (n-1)d\)
Substitute for a1 and d and simplify.

Answer 7

Let's look at A:
3n – 18
n = 1: 3 - 18 = -15
Since the first term is 15, not -15, this can't be it.

Answer 8

Let's look at B:
6(3 - n)
n = 1: 6(3 - 1) = 6 * 2 = 12. Since the first term is 15, not 12, this can't be it.

Answer 9

Do the same for choices C and D.
If with one choice, n = 1 works, then use n = 2, 3, 4, and make sure all of the n values also work.