The first number in the following sequence is 1. It is followed by two 1's and two 2's. This is followed by three 1's, three 2's, and three 3's. The sequence continues in this fashion.

1, 1, 1, 2, 2, 1, 1, 1, 2, 2, 2, 3, 3, 3, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, ... .

Find the 2021st number in this sequence.

Guest Aug 5, 2022

#2**0 **

If you count them, you should see this pattern:

1, 4, 9, 16, 25.........etc. They are squares of the counting numbers, 1, 2, 3, 4, 5.........etc.

If you sum up all the squares up 17, you should get:

1785 + {18 x 13} ==2019 + 2 (14s) ==2021 terms

So, the 2021st term should be: 14

Guest Aug 5, 2022

edited by
Guest
Aug 5, 2022