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

🎥 Watch Detailed Video Solution:

Chaliye isko step by step easy Hinglish me solve karte hain 👇

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.