While sorting some buttons, Shivani put 100 buttons in the first box, 121 buttons in the second box, 144 buttons in the third box, and 169 buttons in the fourth box. What kind of sequence is this?

Answer 1

The number of buttons in each box is as follows:

1. First box: 100 buttons
2. Second box: 121 buttons
3. Third box: 144 buttons
4. Fourth box: 169 buttons

Now, let's identify these numbers:

• 100 is \(10^2\)
• 121 is \(11^2\)
• 144 is \(12^2\)
• 169 is \(13^2\)

The numbers 100, 121, 144, and 169 are perfect squares of consecutive integers starting from 10 to 13.

Therefore, this sequence represents the squares of consecutive integers starting from 10:

• \(10^2, 11^2, 12^2, 13^2\).

In conclusion, the sequence is a sequence of perfect squares of consecutive integers.