Question 3 of 19beginner💡 UnderstandShort Answer3 marks

Why are 1, 3, 6, 10, 15, … called triangular numbers? Why are 1, 4, 9, 16, 25, … called square numbers or squares? Why are 1, 8, 27, 64, 125, … called cubes?

Correct Answer

Triangular Numbers (1, 3, 6, 10, 15, …): Called so because each number can be arranged as dots in the shape of an equilateral triangle. The first triangular number 1 is a single dot. 3 forms a triangle with 2 dots on each side. 6 forms a triangle with 3 dots on each side. And so on.

Square Numbers (1, 4, 9, 16, 25, …): Called squares because each number can be arranged as dots in a perfect square grid. For example, 4 dots form a 2×22 \times 2 square. 9 dots form a 3×33 \times 3 square. 16 dots form a 4×44 \times 4 square.

Cubes (1, 8, 27, 64, 125, …): Called cubes because each number represents the total number of unit cubes needed to form a larger cube. For example, 8 unit cubes form a 2×22 \times 2×2 cube. 27 unit cubes form a 3×33 \times 3×3 cube. 64 unit cubes form a 4×44 \times 4×4 cube.

Exercise: Figure it Out (Section 3) | Q: 2 | (Page Page 5)
For More Understanding

Explanation

The chapter explains in section 1.3 that many number sequences can be visualized using pictures. Table 2 shows pictorial representations where triangular numbers are shown as triangular arrangements of dots, square numbers as square grids of dots, and cubes as three-dimensional arrangements of unit cubes. The names come from these geometric arrangements.

Solution Steps

  1. Triangular numbers can be arranged as dots in an equilateral triangle shape.

  2. Square numbers can be arranged as dots in a perfect square grid.

  3. Cubes represent unit cubes that form larger cubes.

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