1. The following sequence consists of a block of 6 numbers that repeats indefinitely. 1, 4, 2, 5, 7, 8, 1, 4, 2, 5, 7, 8.... Which of the following is the 65th term of the sequence?
Answer: A
The 65th term of the sequence is 2.
To determine the 65th term of the repeating sequence, we can find the position of the term within the cycle by calculating \( 65 \mod 6 \), which gives us a remainder of 5. The 5th term in the sequence 1, 4, 2, 5, 7, 8 is 2.
A) 2
Option A is correct because, when we calculate the position of the 65th term in the repeating block of 6 numbers, we find that the term at this position corresponds to the 5th term in the block, which is indeed 2.
B) 5
Option B is incorrect because the term at the 5th position of the sequence is 7, not 5. Therefore, while 5 is part of the sequence, it does not correspond to the 65th term.
C) 7
Option C is incorrect as well. The 7 appears as the 5th term in the repeating block, but since we are looking for the 65th term, which is calculated to be 2, this option does not reflect the correct placement.
D) 8
Option D is also incorrect. The 8 is the 6th term in the block. Given our calculations indicate that the 65th term corresponds to the 5th position in the sequence, 8 cannot be the correct answer.
Conclusion
The correct answer is definitively 2, as determined by the calculation of \( 65 \mod 6 \), which indicates that the 65th term corresponds to the 5th term in the repeating sequence. All other options fail to match this position within the cycle, confirming that they are incorrect.