jmc

Question

John counts up from 1 to 13, and then immediately counts down again to 1, and then back up to 13, and so on, alternately counting up and down: align* &(1, 2, 3,4,5,6,7,8,9,10,11,12,13, &12,11,10,9,8,7,6,5,4,3,2,1,2,3,4, ). align* What is the 5000^th integer in his list?

Accepted Answer

We can treat this list as a sequence with a repetitive pattern. We see the sequence repeats itself every 24 elements (from 1 to 13 then back to 2). When 5000 is divided by 24, its remainder is 8. Therefore we see the 5000^th integer is the same as the 8^th integer, which is 8.