In the sequence of numbers 1 2 3 4 5 6 7 8 9 2 4 6 8 9 7 5 3 1 9 8 7 6 5 4 3 2 1, which number is third to the left of the number that lies exactly in the middle of the sequence?

Introduction / Context:
In digit sequence reasoning, you are often asked to identify elements relative to a particular reference, such as the middle term or an element from one end. This question combines both ideas: you must first locate the exact middle term of a long sequence and then move a specified number of positions to the left to find the required number.

Given Data / Assumptions:
- The sequence is: 1 2 3 4 5 6 7 8 9 2 4 6 8 9 7 5 3 1 9 8 7 6 5 4 3 2 1. - We must identify the number that is third to the left of the middle element. - Positions are counted from the left, and the sequence length is odd, so there is a single exact middle term.

Concept / Approach:
First, determine the total number of elements in the sequence. For an odd length N, the middle position is (N + 1) divided by 2. Once the index of the middle term is found, move three positions to the left of that index to locate the desired element. Careful counting of positions is more important than any numeric pattern in the digits themselves for this question.

Step-by-Step Solution:
Step 1: Count the number of terms in the sequence. There are 27 terms. Step 2: The middle position for 27 terms is (27 + 1) / 2 = 14. So the 14th term is the middle element. Step 3: Write down the positions with their terms from the left to confirm: Positions 1 to 9: 1, 2, 3, 4, 5, 6, 7, 8, 9. Positions 10 to 18: 2, 4, 6, 8, 9, 7, 5, 3, 1. Positions 19 to 27: 9, 8, 7, 6, 5, 4, 3, 2, 1. Step 4: Identify the 14th term. From the listing, position 14 corresponds to the number 9. Step 5: Now we need the number that is third to the left of this 14th term. Step 6: One position left is 13th term (8), two positions left is 12th term (6), and three positions left is 11th term. Step 7: The 11th term in the sequence is 4. Step 8: Therefore, the number that is third to the left of the middle term is 4.

Verification / Alternative check:
You can verify by writing the sequence with index numbers above or below each digit. When you do this carefully, you will again find that the 14th position holds 9 and that positions 11, 12, and 13 hold 4, 6, and 8 respectively. Moving three steps left from position 14 lands you at position 11, which clearly contains 4. This cross check ensures that no counting or indexing error has occurred.

Why Other Options Are Wrong:
3: The number 3 appears in the sequence but not in the required relative position. 5: This digit is present in several places, yet none of those positions match being third to the left of the middle term. 7: This digit also occurs, but confirming positions shows it is not three places left of the middle element.

Common Pitfalls:
Students sometimes miscount the total terms, leading to an incorrect middle position. Others confuse "third to the left" with "third from the left," which is a completely different reference. A careful habit is to mark the middle term first, then physically count left or right as required, rather than trying to jump directly to a mental answer.

Final Answer:
The number that is third to the left of the middle term of the sequence is 4.