Math Problem Statement

How many tiles are there in the 7th pattern?

Solution

The image shows a sequence of patterns made from tiles, where the same number of tiles is added each time. Based on the provided pattern numbers (1, 2, 3, and 4), you are tasked with determining how many tiles are in the 7th pattern.

Upon examining the patterns:

  • The 1st pattern contains 1 tile.
  • The 2nd pattern contains 4 tiles.
  • The 3rd pattern contains 9 tiles.
  • The 4th pattern contains 16 tiles.

It appears that each pattern is forming a square number, following the sequence 1^2, 2^2, 3^2, 4^2, etc.

The formula for the number of tiles in the nth pattern is n2n^2, where nn is the pattern number.

For the 7th pattern: 72=497^2 = 49

Therefore, the 7th pattern contains 49 tiles.

Would you like any further details or explanations? Here are some related questions to explore further:

  1. How do you derive the general formula for the nth pattern?
  2. What is the sum of the tiles for the first 7 patterns?
  3. How would this sequence change if each pattern added a different number of tiles?
  4. Can you describe how this pattern might be represented graphically?
  5. How can square numbers be applied in real-life scenarios?

Tip: Recognizing patterns in sequences like this can help you solve similar problems quickly and build a deeper understanding of mathematical concepts like square numbers.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Arithmetic Sequences
Square Numbers
Pattern Recognition

Formulas

n^2, where n is the pattern number

Theorems

Properties of Square Numbers

Suitable Grade Level

Grades 6-8