Video narration
3, 7, 11... sankhya rekha par har baar chaar ki barabar chhalaang hai. To dasvaan pad aur pehle das padon ka kul yog, saare pad likhe bina, kaise nikaalenge? Aise kram ko arithmetic progression, yaani AP, kehte hain: lagataar padon ka antar samaan rehta hai. Pehla pad a hai - yahaan 3. Har baar judne wala samaan antar, common difference d, yahaan 4 hai. n padon ki sankhya hai, antaron ki nahin; l aakhiri pad hai. Antar samaan ho to saare pad likhne ki zaroorat nahin. nth term ka sootra: a_n = a + (n - 1)d. n-1 isliye, kyunki n padon ke beech n-1 antaral hote hain. Yog ke do roop: S_n = n/2(a + l), jahaan l aakhiri pad hai; ya S_n = n/2[2a + (n - 1)d]. Yahaan a_10 = 3 + 9*4 = 39. Phir S_10 = 10/2(3 + 39) = 210; doosre roop se 10/2[6 + 9*4] = 210. To niyam chaar jodna hai: dasvaan pad 39, pehle das padon ka yog 210.