30. 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: C
The 65th term of the sequence is 7.
To determine the 65th term of the repeating sequence, we can find the position of the term within the repeating block of 6 numbers. By calculating 65 modulo 6, we find that 65 leaves a remainder of 5, indicating that the 65th term corresponds to the 5th position in the block.
A) 2
Option A is incorrect because 2 is the 3rd term in the repeating sequence. The 3rd position does not align with the 5th position determined by the modulo operation.
B) 5
Option B is also incorrect as 5 is the 4th term in the sequence. This selection does not match the 5th position we identified for the 65th term.
C) 7
Option C is correct since 7 is indeed the 5th term in the repeating block. By calculating 65 modulo 6, we see that the remainder is 5, which corresponds to the 5th term, confirming that 7 is the correct answer.
D) 8
Option D is incorrect because 8 is the 6th term in the sequence. Since the 65th term matches the 5th position, 8 does not satisfy the criteria for the correct answer.
Conclusion
The 65th term of the sequence is definitively 7, as it corresponds to the 5th position in the repeating block. All other options fail to match this position, confirming that they cannot be the correct answer. The understanding of modular arithmetic is key in identifying the correct term in a repeating sequence.