Which term of the AP : 3, 15, 27, 39, . . . will be 132 more than its 54th term?

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Given Data

AP: 3, 15, 27, 39, …

First term (a) = 3

Common difference (d) = 15 − 3 = 12

Formula of nth term:

aₙ = a + (n−1)d

Jaha:

a = first term

d = common difference

n = term number

Step 1: Find 54th Term

Formula lagate hain:

a54 = 3 + (54 - 1) × 1

a54 = 3 + 53 × 12

a54 = 3 +636

a54 = 639

So, 54th term = 639

Step 2: According to Question

Humein woh term find karni hai jo 54th term se 132 more ho.

Matlab:

Required term = 639 + 132

= 771

Ab hume find karna hai kaunsa term 771 ke equal hai.

Step 3: Find n

Formula use karte hain:

771 = 3 + (n - 1)12

771 - 3 = (n - 1)12

768 = (n - 1)12

n - 1 = 64

n = 65

Final Answer

✅ 65th term of the AP is 132 more than its 54th term.

Quick Revision Points

AP nth term formula: aₙ = a + (n − 1)d

Pehle 54th term nikala

Phir usme 132 add kiya

Fir nth term formula se n find kiya

FAQs

Q1. Arithmetic Progression kya hoti hai?

Jisme consecutive terms ke beech difference same ho, usse AP kehte hain.

Q2. AP ka nth term ka formula kya hai?

aₙ = a + (n − 1)d

Q3. Is question me common difference kya tha?

Common difference = 12

Q4. 54th term kitni thi?

54th term = 639

Q5. Required term kaun si thi?

65th term

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

The 17th term of an AP exceeds its 10th term by 7. Find the common difference.

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

📌 Question

The 17th term of an AP exceeds its 10th term by 7. Find the common difference.

✏️ Concept Used – Arithmetic Progression (AP)

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

17th term 10th term se 7 zyada hai.

Mathematically:

a17 - a10 = 7

🔹 Step 2: Formula Apply Karein

a17 = a + 16d

a10 = a + 9d

Ab difference nikalte hain:

 (a + 16d) -   (a + 9d) = 7

🔹 Step 3: Solve Karein

a + 16d - a - 9d = 7

7d = 7

d = 1

✅ Final Answer:

👉 Common Difference (d) = 1

📚 Short Trick (Exam Friendly Method)

Direct formula use karo:

an - am = (n - m)d

Yaha:

a17 - a10 = (17- 10)d

7 = 7d

d = 1

Ye method fast aur time-saving hai board exams ke liye ✅

❓ FAQs

Q1. AP me common difference kaise nikalte hain?

Do terms ka difference le kar formula apply karte hain:

aₙ − aₘ = (n − m)d

Q2. Kya first term ki value jaroori thi?

Nahi, kyunki question me sirf difference diya gaya tha.

Q3. Ye question board exam me aa sakta hai?

Haan, ye Class 10 Maths ke important AP questions me se ek hai.

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

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