Answer:
[tex] a_n = 12 - 3n [/tex]
Step-by-step explanation:
The first term is 9.
Term 1 is 9.
Term 2 is 9 - 3.
Term 3 is 9 - 2(3).
Term 4 is 9 - 3(3).
Term 5 is 9 - 4(5)
Notice the pattern in terms 3 through 5. For each term, subtract 1 less than the term number multiplied by 3 from 9.
For term n, you subtract 1 less than n times 3 from 9.
The nth term is 9 - (n - 1) * 3
[tex] a_n = 9 - (n - 1) \times 3 [/tex]
Now we simplify the expression on the right side.
[tex] a_n = 9 - 3(n - 1) [/tex]
[tex] a_n = 9 - 3n + 3 [/tex]
The expression for the nth term is
[tex] a_n = 12 - 3n [/tex]
Let's see if it works.
n = 1
[tex] a_n = 12 - 3(1) = 12 - 3 = 9 [/tex]
n = 2
[tex] a_n = 12 - 3(2) = 12 - 6 = 6 [/tex]
n = 3
[tex] a_n = 12 - 3(3) = 12 - 9 = 3 [/tex]
n = 4
[tex] a_n = 12 - 3(4) = 12 - 12 = 0 [/tex]
n = 5
[tex] a_n = 12 - 3(5) = 12 - 15 = -3 [/tex]
n = 6
[tex] a_n = 12 - 3(6) = 12 - 18 = -6 [/tex]
As you can see, following this rule fro the nth term, we got the same first siz terms you got above. Our answer is correct.
Answer: [tex] a_n = 12 - 3n [/tex]
