Final Answer:
The sequence alternates between decreasing (10, 35, 34, 35) and increasing (12, 32, 9) patterns. Following the established patterns, the next pair is 9 and 35. Thus the correct option is 3) 9 35.
Step-by-step explanation:
The given sequence appears to consist of two alternating patterns. The first pattern is a decreasing sequence: 10, 35, 34, and 35. The second pattern is an increasing sequence: 12, 32, and 9. Following this pattern, the next pair should be a continuation of the second pattern, which is 9 and 35. Therefore, the correct answer is option 3) 9 35.
Now, let's delve into the explanation. The sequence alternates between two sets of numbers. The first set, 10, 35, 34, and 35, is decreasing and follows a pattern where each number is either 1 less or 1 more than the previous one. The second set, 12, 32, and 9, is increasing and follows a pattern where each number is either 20 less or 23 more than the previous one. Recognizing these patterns helps identify the next pair in the sequence, which is 9 and 35.
In mathematical terms, the first pattern can be expressed as x, x-1, x-2, x-1, and the second pattern as y, y-20, y+23. Applying these patterns to the last known numbers (9 and 35) in the sequence confirms that the next pair should be 9 and 35.
Therefore, option 3) 9 35 is the correct answer based on the observed patterns in the sequence.