To solve the problem, we first identify the pattern in the sequence and group the terms into segments.
Step 1: Identify the pattern
The sequence is grouped into segments where each segment of length 5 starts with (k) and follows:
(k, k+1, k+2, k+1, k)
For example:
- Group 1 ((k=1)): 1,2,3,2,1
- Group 2 ((k=2)): 2,3,4,3,2
- Group 3 ((k=3)): 3,4,5,4,3
Each group has 5 terms.
Step 2: Find the group of the 2018th term
Each group has 5 terms. To find the group number (G):
(G = \left(\frac{2018-1}{5}\right) + 1 = \left(\frac{2017}{5}\right) +1 = 403 +1 = 404)
The 2018th term is in Group 404.
Step 3: Find the position within the group
The offset in the group is:
(2018 - (404-1)*5 = 2018 - 2015 = 3)
The third term in Group (k) is (k+2). For Group 404:
(404 + 2 = 406)
Answer: (\boxed{406})


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