Number sequences ke aapas mein rishte

Class 6 Maths · Chapter 1: Patterns in Mathematics · NCERT Ganita Prakash section 1.4

Seekho

1 square se shuru karo.

1 = 1 × 1

Iske chaaron taraf 3 squares ka L lagao. Ab ye 2 × 2 square hai.

1 + 3 = 4 = 2 × 2

5 ka L lagao. Ab ye 3 × 3 hai.

1 + 3 + 5 = 9 = 3 × 3

Khud karke dekho: layers jodo aur square ko badhte dekho.

Har naya L 2 bada hai, to L's odd numbers hain. Pehle n odd numbers jodne se hamesha n × n square banta hai.

1 + 3 + 5 + 7 + 9 = 25 = 5 × 5

Ek aur pattern: upar aur neeche gino. 1 + 2 + 3 + 4 + 3 + 2 + 1. Dots ko dekho, ye 4 × 4 square mein fit ho jaate hain.

1 + 2 + 3 + 4 + 3 + 2 + 1 = 16 = 4 × 4

Lagataar do triangular numbers jodo: blue triangle (15) aur coral triangle (10) milkar ek square bana dete hain.

10 + 15 = 25 = 5 × 5

2 ki powers jodo: 1, 1 + 2, 1 + 2 + 4 … Total hamesha agli power of 2 se ek kam hota hai. Dashed box wahi 1 hai jo kam hai.

1 + 2 + 4 + 8 = 15 = 16 − 1

Hexagonal numbers jodo to cube numbers milte hain! Har hexagonal number cube ki ek dikhne wali parat hai.

1 + 7 + 19 + 37 = 64 = 4 × 4 × 4

Yaad rakho

• Pehle n odd numbers ka jod n × n hai.
• 1 + 2 + … + n + … + 2 + 1 = n × n.
• Lagataar do triangular numbers ka jod square number hai.
• 1 + 2 + 4 + 8 + … agli power of 2 se ek kam hai.

Quick check

1 + 3 + 5 + 7 + 9 + 11 + 13 = ?

1. 42
2. 45
3. 49
4. 56

Socho

Pehle 12 odd numbers ka jod kya hai? Kya ek-ek jode bina nikaal sakte ho?

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.