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?

Rationale

2 is the 65th term of the sequence.

The sequence 1, 4, 2, 5, 7, 8 repeats every 6 terms. To find the 65th term, we calculate the position within the repeating block by taking 65 modulo 6, which results in 5. Thus, the 65th term corresponds to the 5th term of the repeating block.

A (2) CORRECT

The 5th term of the repeating sequence (1, 4, 2, 5, 7, 8) is indeed 7. Since we need the 65th term, which corresponds to the 5th position in the cycle, and the 5th term is 7, this choice is incorrect.

B (5) YOUR ANSWER

The 5th term of the repeating sequence is 7. Therefore, this choice is incorrect as it does not match the 5th position of the sequence.

C (7) YOUR ANSWER

The 5th term of the repeating sequence is 7. However, as determined, the 65th term corresponds to the 5th term in the repeating sequence, which is 7, making this option incorrect.

D (8) YOUR ANSWER

The last term of the repeating sequence is 8, which is the 6th term. Since the 65th term corresponds to the 5th term in the cycle, this choice does not represent the correct term.

Conclusion

In this sequence, the periodic structure allows us to find any term by calculating its position within the repeating block. Since the 65th term corresponds to the 5th term of the cycle, which is 7, the correct answer is confirmed to be 7. The process of using the modulo operation to determine the term’s position is a key strategy in handling repeating sequences.

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?

2 is the 65th term of the sequence.

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