Question

To go to sleep, Oliver counted by 6s starting from 15. Thus the first few numbers he named were 15,21,27,33,... The last number he named before he fell asleep was 363. How many numbers did Oliver name?

Answer 1

59

Explanation:

If we subtract 9 from each number Oliver named, we get the new list

6, 12, 18, 24, ..., 354,

which consists of the multiples of 6 from 1 ∙ 6 through 59 ∙ 6. There are clearly 59 of these, so Oliver named 59 numbers (namely: 1 ∙ 6 + 9, 2 ∙ 6 + 9, 3 ∙ 6 + 9, and so on through 59 ∙ 6 + 9).

Answer 2

We can use the explicit formula to figure this out.


`f(n)=f(1)+d(n-1)`

f(1) means the first term, which is 15.
d represents the common difference, which is 6.

f(n) = 15 + 6(n - 1)
f(n) = 15 + 6n - 6
f(n) = 6n + 9

363 = 6n + 9
Subtract 9 from both sides.
354 = 6n
Divide both sides by 6.
59 = n

Olvier named 59 numbers.