Hey Math Whiz! Check out how these blocks are arranged. Can you figure out the pattern and answer the questions?
Let's Break Down the Pattern!
Visual Pattern:
- Term 1: Has 1 block. This is a 1x1 square. (1 × 1 = 1)
- Term 2: Has 4 blocks. This is a 2x2 square. (2 × 2 = 4)
- Term 3: Has 9 blocks. This is a 3x3 square. (3 × 3 = 9)
The pattern is that each term forms a square where the side length is equal to the term number!
Answering the Questions:
1. Term 4:
Following the pattern, Term 4 would be a 4x4 square. So, it would have 4 × 4 = 16 blocks.
2. Term 7:
For Term 7, it would be a 7x7 square. So, it would have 7 × 7 = 49 blocks.
3. Formula for Term 'n':
If 'n' is the term number, the number of blocks is 'n' multiplied by 'n'. This is written as n × n or n² (n squared).
- For n=1: 1 × 1 = 1 block
- For n=2: 2 × 2 = 4 blocks
- For n=3: 3 × 3 = 9 blocks
- And so on...
This is why n × n is the correct formula!