Pattern Pakdo, Rishte Kholo

Class 7 Maths · Chapter 4: Letter-Numbers wale Expressions · NCERT Ganita Prakash section 4.5

Seekho

Formula jaasoos: ek number machine do number leti hai aur ek deti hai: (5, 2) → 8, (8, 1) → 15, (9, 11) → 7. "Pehle ka do guna minus doosra" aazmaao: 2 × 5 − 2 = 8 ✓, 2 × 8 − 1 = 15 ✓, 2 × 9 − 11 = 7 ✓. Iska formula 2a − b. Apni machine banaakar dost ko chunauti do!

2a − b

Dohraate designs: ek border A, B, C, A, B, C … dohraata hai. C sthaan 3, 6, 9 … par, to uska nth baar 3n par; B ek pehle, 3n − 1 par; A 3n − 2 par. Sthaan 122 par kaunsa? 122 ÷ 3 ka shesh 2, jaise sthaan 2 → B. Shesh 0 matlab C, aur 1 matlab A.

C: 3n · B: 3n − 1 · A: 3n − 2

Calendar ka jaadu: tareekhon ke kisi bhi 2 × 2 varg mein upar-baayein a ho, to baaki a + 1, a + 7 aur a + 8. Vikarnon ke jod a + (a + 8) = 2a + 8 aur (a + 1) + (a + 7) = 2a + 8: hamesha barabar! Algebra ise har varg ke liye ek saath saabit karta hai, jo kuch varg jaanchne se kabhi nahi hota.

a + (a + 8) = (a + 1) + (a + 7) = 2a + 8

Tiliyon ke tribhuj: 1, 2, 3, 4 … tribhujon ki kataar mein 3, 5, 7, 9 … tiliyan: har baar 2 zyaada. Step y mein 3 plus (y − 1) do: 3 + 2(y − 1), jo saral hokar 2y + 1. To step 33 mein 67 tiliyan aur step 108 mein 217, ek bhi banaaye bina!

3 + 2(y − 1) = 2y + 1

Explore: kaunsa design kahan?

1. Border A, B, C dohraata hai. Har sthaan ko uske design se sort karo.

Yaad rakho

• Pehle pattern shabdon mein, phir expression mein (C 3n par, B 3n − 1 par, …).
• Algebra dikhaata hai pattern har sthiti mein chalta hai: 2 × 2 calendar ke dono vikarn 2a + 8.

Quick check

2y + 1 se tribhuj kataar ke step 10 mein kitni tiliyan?

1. 21
2. 20
3. 30
4. 12

Socho

Ek baar modkar kaatne se rassi ke 3 tukde, do baar se 5. r baar modne ka niyam kya hai?

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.