The sequence 2, 3, 5, 6, 7, 10, 11, contains all the positive integers from least to greatest that are neither squares nor cubes. What is the 500th term of the sequence?

Guest Dec 23, 2021

#1**+1 **

We can start witht the number 500 and count all of the squares/cubes under that.

22^{2} (484) is the __closest we can get to 500 without going over it.__

7^{3} (343) os the __closest we can get to 500 without going over it.__

22+7 is 29, which is how many we got rid of (almost, but not really)

Since 1 is both a __square and a cube__, we need to subtract 1 for the double count.

Since 64 is both a

So to compensate for each square and cube not included, we can add 27 (29-2) to 500

The 500th term *would* *be* 527, but 512 is 8^3, so we also have to compensate for that.

527+1=528

Guinevere Dec 23, 2021