Aaj hum Class 10 Maths – Arithmetic Progression (AP) ka ek important question solve karne wale hain jo exams me frequently pucha jata hai.

📌 Question:

If the 3rd and the 9th terms of an AP are 4 and –8 respectively, which term of this AP is zero?

✏️ Concept Used – Arithmetic Progression (AP)

Arithmetic Progression (AP) me nth term ka formula hota hai:

aₙ = a + (n−1)d

Jaha:

a = first term

d = common difference

n = term number

🧮 Step by Step Solution

🔹 Step 1: Given Information

3rd term = 4

9th term = –8

Formula ke according:

a3= a + 2d = 4

a9 = a + 8d = -8

🔹 Step 2: Dono Equations ko Solve karein

Equation (1):

a + 2d = 4

Equation (2):

 a + 8d = -8

Ab Equation (2) – Equation (1):

(a + 8d) - (a + 2d) = -8 -4

6d = -12

d = -2

🔹 Step 3: d ki Value Equation (1) me Put karein

a + 2(-2) = 4

a - 4 = 4

a = 8

🔹 Step 4: Kaunsa Term Zero Hai?

Ab formula lagayenge:

aₙ = a + (n−1)d

aₙ = 8 + (n−1)(-2)

aₙ = 8 -2(n−1)d

Ab zero ke equal karte hain:

 8 - 2(n - 1) = 0

8 - 2n + 2 = 0

10 - 2n = 0

2n = 10

n = 5

✅ Final Answer:

👉 5th term of the AP is zero.

📚 Final Summary

First term (a) = 8

Common difference (d) = -2

Zero term position = 5th term

❓ FAQs

Q1. AP ka nth term ka formula kya hota hai?

Nth term ka formula hota hai:

aₙ = a + (n−1)d

Q2. Common difference kaise nikalte hain?

Do different terms ka difference le kar equations solve karte hain.

Q3. Kya ye question board exam me aa sakta hai?

Haan, ye type ka question Class 10 Maths board exam me kaafi baar pucha gaya hai.

👉 Agar aap AP ke aur bhi similar questions practice karna chahte hain, to is question ka detailed solution bhi dekhein:

An AP Consists of 50 Terms, 3rd Term is 12 and Last Term is 106 – Find the 29th Term