Answer: -9n+20
This is the same as 20-9n
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Explanation:
The jump from 11 to 2 is "minus 9"
The jump from 2 to -7 is also "minus 9".
Assuming this pattern continues on, we have an arithmetic sequence with
- a = 11 = first term
- d = -9 = common difference
The nth term can be found like so
[tex]a_n = a + d(n-1)\\\\a_n = 11 + (-9)(n-1)\\\\a_n = 11 -9n + 9\\\\a_n = -9n+20\\\\[/tex]
Let's check the answer by trying n = 3
[tex]a_n = -9n+20\\\\a_3 = -9*3+20\\\\a_3 = -27+20\\\\a_3 = -7\\\\[/tex]
This shows the third term is -7, which matches what the original sequence shows. The answer is partially confirmed. I'll let you check the other values of n. You should get 11 when trying n = 1, and you should get 2 when trying n = 2.
