Number sequences ki pictures

Class 6 Maths · Chapter 1: Patterns in Mathematics · NCERT Ganita Prakash section 1.3

Seekho

Bahut si sequences pictures mein banaayi ja sakti hain, aur picture se pattern dikhta hai. Triangular numbers dots ke triangles banate hain. Har nayi picture mein ek nayi line (coral) judti hai, jo ek dot lambi hoti hai.

1 + 2 + 3 + 4 + 5 = 15

Square numbers dots ke squares banate hain. 4 × 4 se 5 × 5 square banane mein ek L-shape border (coral) judta hai. Isliye inhe squares kehte hain.

5 × 5 = 25

Cube numbers chhote blocks se cube banate hain. 3 blocks chauda, 3 gehra aur 3 ooncha cube 27 blocks ka hota hai.

3 × 3 × 3 = 27

Kuch numbers do tarah se draw ho sakte hain. 36 dots 8 rows ka triangle banate hain, aur 6 by 6 ka square bhi. To 36 triangular number aur square number dono hai.

Hexagonal numbers: 1, 7, 19, 37 … Har nayi ring poore chaaron taraf aati hai (coral). Rings mein 6, 12, 18 … dots hain. Agla hexagonal number 37 + 24 = 61 hai.

1 + 6 + 12 + 18 = 37

2 ki powers ki pictures: har picture pichhli picture ki do copies hai: 1, 2, 4, 8, 16.

Explore: dot pictures khud banao. Row jodo ya hatao aur dots gino.

1. 10 dots wala triangle banao.
2. 25 dots wala square banao.
3. Hexagonal number 19 banao.

Yaad rakho

• Pictures se dikhta hai ki sequence aise kyon badhti hai.
• Triangular numbers triangles banate hain, square numbers squares, cube numbers cubes.

Quick check

6 lines wali triangle picture mein kitne dots hain?

1. 18
2. 21
3. 28
4. 36

Socho

Kya 21 triangular number hai? Kya ye square number hai? Dots se banakar jaancho.

Practice

Teen levels (easy, medium, hard) ke naye sawaalon se practice karo, kuch hands-on, hints aur hal ke saath. Topic poora karne ke liye pichhle 5 mein se 4 sahi karo.