Question

Which answer is the explicit rule for the sequence 5, 11, 17, 23, 29 ...?

1) an = -1 - 6n
2) an = -1 + 6n
3) an = 1 - 6n
4) an = 1 + 6n

Answer 1

The explicit rule for the sequence 5, 11, 17, 23, 29... is 'an = -1 + 6n', which can also be written as 'an = 6n - 1'. This is an arithmetic sequence with a common difference of 6.

Step-by-step explanation:

The sequence in the question increases by a constant difference of 6 (since 11 - 5 = 6, 17 - 11 = 6, and so on), which suggests that it is an arithmetic sequence. The general form of an arithmetic sequence is an = a1 + (n - 1)d, where an is the n-th term, a1 is the first term, n is the term number, and d is the common difference between terms. In this case, a1 is 5 and d is 6, so the explicit rule is an = 5 + (n - 1) × 6, which simplifies to an = 6n - 1. This corresponds to option 2) an = -1 + 6n, which is equivalent to an = 6n - 1.