+0

To go to sleep, Oliver counted by 6s starting from 15. Thus the first few numbers he named were

0
573
2

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?

May 8, 2018

#1
+2

[L - F] / D + 1=N, where L=Last term, F=First term, D=Common difference, N=Number of terms

[363 - 15] / 6 + 1 =59 terms or numbers that Oliver counted.

May 8, 2018
#2
+1

If he named 1 number, then the last number he named would be 15

If he named 2 numbers, the last number he named would be 15 + 6

If he named 3 numbers, the last number he named would be 15 + 6 + 6

If he named 4 numbers, the last number he named would be 15 + 6 + 6 + 6  which is  15 + 6(4 - 1)

So... if he named  n  numbers, the last number he named would be  15 + 6(n - 1)

They tell us the last number he named was  363 . So..

363  =  15 + 6(n - 1)    Subtract  15  from both sides.

348  =  6(n - 1)            Divide both sides by  6 .

58  =  n - 1                  Add  1  to both sides.

59  =  n

May 8, 2018
edited by hectictar  May 8, 2018