Question
While sorting some buttons, Elizabeth put 169 buttons in the first box, 196 buttons in the second box, 225 buttons in the third box, and 256 buttons in the fourth box. What kind of sequence is this?
Answers
GPT-4o mini
To determine the type of sequence formed by the numbers of buttons in the boxes, let's analyze the numbers provided: 169, 196, 225, and 256.
We can check whether these numbers are perfect squares:
- \(169 = 13^2\)
- \(196 = 14^2\)
- \(225 = 15^2\)
- \(256 = 16^2\)
The numbers correspond to the squares of consecutive integers: \(13, 14, 15,\) and \(16\).
This means that the sequence is a sequence of perfect squares of consecutive integers. Specifically, it can be defined as \(n^2\) where \(n\) is an integer starting from 13 and ending at 16. This is neither an arithmetic sequence nor a geometric sequence, but a sequence of perfect squares of consecutive natural numbers.
We can check whether these numbers are perfect squares:
- \(169 = 13^2\)
- \(196 = 14^2\)
- \(225 = 15^2\)
- \(256 = 16^2\)
The numbers correspond to the squares of consecutive integers: \(13, 14, 15,\) and \(16\).
This means that the sequence is a sequence of perfect squares of consecutive integers. Specifically, it can be defined as \(n^2\) where \(n\) is an integer starting from 13 and ending at 16. This is neither an arithmetic sequence nor a geometric sequence, but a sequence of perfect squares of consecutive natural numbers.