An AP Consists of 50 Terms, 3rd Term is 12 and Last Term is 106 – Find the 29th Term | Class 10 Maths Solution

📘 Chapter: Arithmetic Progression (AP)
📚 Class: 10th Mathematics (NCERT Based)

Aaj hum solve karenge ek important board level question:

An AP consists of 50 terms of which the 3rd term is 12 and the last term is 106. Find the 29th term.

🎥 Watch Detailed Video Solution:

Yeh question Class 10 Maths – Arithmetic Progression chapter se hai aur exams me frequently poocha jata hai.

🔎 Step 1: Use nth Term Formula

AP ka formula hota hai:

an = a + (n-1)d

Hume diya hai:

a3 = 12

a50 = 106

🔎 Step 2: Formula Apply Karein

3rd Term ke liye:

a + 2d = 12 (equation 1)

50th Term ke liye:

a + 49d = 106 (equation 2) 

🔎 Step 3: Subtract Equation 1 from Equation 2

🔎 Step 4: Find First Term (a)

Equation 1 me d = 2 put karte hain:

a + 2(2) = 12

a + 4 = 12

a = 8

🔎 Step 5: Find 29th Term

Formula:

a29 = a + 28d

a29 = 8 + 28(2)

a29 = 8 + 56

a29 = 64

🎯 Final Answer:

👉 29th term of the AP is 64.

📝 Exam Writing Tip

Board exam me: ✔ Dono equations clearly likhein

✔ Proper subtraction dikhayein

✔ d aur a dono calculate karein

✔ Final answer box me likhein

❓ Frequently Asked Questions (FAQs)

1️⃣ What is given in the question “An AP consists of 50 terms, 3rd term is 12 and last term is 106”?

In this question, we are given:

Total number of terms (n) = 50

3rd term (a₃) = 12

Last term (a₅₀) = 106

We need to find the 29th term (a₂₉).

2️⃣ What formula is used to find any term in an Arithmetic Progression?

The formula to find the nth term of an AP is:

an = a + (n-1)d

Where

a = first term

d = common difference

n = term number

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

Find the 31st Term of an AP Whose 11th Term is 38 and 16th Term is 73.