Discussion
Which of the following number is in the list of numbers 5, 11, 17, 23, ... ?
Answer: A
The number in the list is 179.
The list 5, 11, 17, 23, ... increases by 6, so every term is one less than a multiple of 6: the nth term is 6n - 1. A number belongs to the list if adding 1 gives a multiple of 6.
\[ \begin{aligned} 179 + 1 &= 180 = 6 \times 30 \\ 189 + 1 &= 190,\ 169 + 1 = 170,\ 159 + 1 = 160 \end{aligned} \]
Only 180 is divisible by 6, so 179 is the 30th term. 190, 170 and 160 leave remainders when divided by 6, so 189, 169 and 159 are not in the list.
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