MathsKhaga · Class 6-8
Pattern se rule, rule se algebra
3, 5, 7, 9... ka 50wan number bina saare likhe kaise nikaloge?
Socho pehle… phir dekho jawab
Ek formula banao! Is pattern ka n-wan number 2n + 1 hota hai. Yahi algebra ki shuruaat hai: pattern ko akshar (variable) mein likhna.
Pattern ko dhyan se dekho: 3, 5, 7, 9 mein har baar 2 badhta hai. Pehla number 3 = 2 x 1 + 1, doosra 5 = 2 x 2 + 1, teesra 7 = 2 x 3 + 1. Isliye n-wan number 2n + 1 hai. Yahan n position batata hai: 1wan, 2wan, 3wan... Isse 50wan number 2 x 50 + 1 = 101 mil jaata hai.
Rozmarra ka example: maan lo ek pencil 5 rupaye ki hai (yeh sirf ek example hai). n pencil ka daam 5n rupaye hoga, kyunki pattern 5, 10, 15 aise hi badhta hai.
Dhyan rakho: formula tab hi bharosemand hai jab usse saare diye hue numbers sahi nikalein. Isliye hamesha ek-do numbers par jaanch kar lo, jaise 4wan number 2 x 4 + 1 = 9 hai.
Ghar pe try karo
Pattern 4, 7, 10, 13 ka rule dhoondo: har baar kitna badhta hai? Phir n-wan number ka formula banao aur 10wan number nikalo. Dobara jaanch karo ki 3rd number sahi aaya.
Wow!
Ek chhota sa formula 2n + 1 hazaaron numbers ek saath bata deta hai!
3 sawaal
- 3, 5, 7, 9 ka 10wan number kya hoga (n-wan number 2n + 1)?
Jawab dekho
21. 2 x 10 + 1 = 21.
- 4, 7, 10, 13 ka n-wan number kaunsa formula hai?
Jawab dekho
3n + 1. Har baar 3 badhta hai aur pehla number 4 = 3 x 1 + 1, isliye 3n + 1.
- Formula mein n kis cheez ka naam hai?
Jawab dekho
Number ki position ka. n batata hai ki yeh pattern ka kaun sa number hai: 1wan, 2wan, 3wan...
NCERT se jodo: NCERT Class 6 Maths — patterns; NCERT Class 7 Maths — algebraic expressions