If the 9th term of a AP be zero, then the ratio of its 29th and 19" terms W1:2 3:1 @1:3 @)3:1

Concept samjho

1. Arithmetic Progression (AP) ka nᵗʰ term hota hai
   $a_n = a + (n-1)d$
   yahan $a$ = first term, $d$ = common difference.
2. Question bolta hai 9ᵗʰ term 0 hai, yaani
   $a_9 = a + 8d = 0$
   isse milta hai $a = -8d$.
3. Ab 29ᵗʰ aur 19ᵗʰ terms likho:
   $a_{29} = a + 28d$
   $a_{19} = a + 18d$
4. $a$ ki jagah (-8d) daal do, simplify karo, ratio lo – bas jawab mil gaya.

Socho ek number-line par hum equal gap wale numbers likh rahe hain – ise hi Arithmetic Progression (AP) kehte hain.
Agar 9ᵗʰ number khud 0 aa gaya, to iska matlab pehla number (start) aur gap (common difference) ke beech ek simple relation ban gaya.
Phir hum 29ᵗʰ aur 19ᵗʰ numbers nikaal kar unka ratio (bhaag) puchte hain.
Jitna aasan dikh raha hai, utna hi aasan hai – bas teen line ki calculation se answer aa jata hai!

Step-by-Step Solution

1. 9ᵗʰ term ki condition:
   $a_9 = a + 8d = 0$
   $\Rightarrow a = -8d$
2. 29ᵗʰ term:
   $a_{29} = a + 28d$
   $= -8d + 28d = 20d$
3. 19ᵗʰ term:
   $a_{19} = a + 18d$
   $= -8d + 18d = 10d$
4. Ratio (29ᵗʰ : 19ᵗʰ):
   $\frac{a_{29}}{a_{19}} = \frac{20d}{10d} = 2$
   Iska matlab $a_{29} : a_{19} = 2 : 1$
   Final Answer: $\boxed{2 : 1}$