Class 10 Maths Chapter 5 Arithmetic Progressions

Class 10 Maths Chapter 5 Arithmetic Progressions – Exercise 5.2 NCERT Solutions

Introduction

Exercise 5.2 focuses on finding the nth term of an Arithmetic Progression (AP). The nth term formula helps us locate any term in the sequence without listing all previous terms. This exercise builds the foundation for solving AP problems in higher mathematics and real‑life applications.

Formula Used

nth Term of AP:

an=a+(n−1)d

Where:

$a$ = first term
$d$ = common difference
$n$ = term number

NCERT Questions with Solutions (10)

Q1. Find the 10th term of AP: 2, 7, 12, …

Solution: $a = 2, d = 5$ . $a_{10} = 2 + (10 - 1) \cdot 5 = 47$ .

Q2. Find the 15th term of AP: 1, 3, 5, …

Solution: $a = 1, d = 2$ . $a_{15} = 1 + (15 - 1) \cdot 2 = 29$ .

Q3. Find the 20th term of AP: 5, 10, 15, …

Solution: $a = 5, d = 5$ . $a_{20} = 5 + (20 - 1) \cdot 5 = 100$ .

Q4. Find the 25th term of AP: -3, -1, 1, …

Solution: $a = - 3, d = 2$ . $a_{25} = - 3 + (25 - 1) \cdot 2 = 45$ .

Q5. Find the 12th term of AP: 10, 7, 4, …

Solution: $a = 10, d = - 3$ . $a_{12} = 10 + (12 - 1) (- 3) = - 23$ .

Q6. Find the 30th term of AP: 3, 6, 9, …

Solution: $a = 3, d = 3$ . $a_{30} = 3 + (30 - 1) \cdot 3 = 90$ .

Q7. Find the 18th term of AP: 8, 14, 20, …

Solution: $a = 8, d = 6$ . $a_{18} = 8 + (18 - 1) \cdot 6 = 110$ .

Q8. Find the 50th term of AP: 1, 4, 7, …

Solution: $a = 1, d = 3$ . $a_{50} = 1 + (50 - 1) \cdot 3 = 148$ .

Q9. Find the 22nd term of AP: 100, 97, 94, …

Solution: $a = 100, d = - 3$ . $a_{22} = 100 + (22 - 1) (- 3) = 37$ .

Q10. Find the 40th term of AP: 0, 10, 20, …

Solution: $a = 0, d = 10$ . $a_{40} = 0 + (40 - 1) \cdot 10 = 390$ .

FAQs (10 from NCERT)

Q: What is the nth term formula of AP? A: $a_{n} = a + (n - 1) d$ .
Q: What is the first term in AP? A: The starting number, denoted by $a$ .
Q: What is the common difference? A: The difference between consecutive terms.
Q: Can nth term be negative? A: Yes, if common difference is negative.
Q: Can nth term be zero? A: Yes, depending on values of $a, d, n$ .
Q: What is the 1st term formula? A: $a_{1} = a$ .
Q: What is the 2nd term formula? A: $a_{2} = a + d$ .
Q: What is the 3rd term formula? A: $a_{3} = a + 2 d$ .
Q: Why is nth term formula important? A: It helps find any term directly.
Q: Why is this exercise important? A: It builds skills for solving AP problems quickly.

Conclusion

Exercise 5.2 has 10 solved questions and 10 FAQs that strengthen your understanding of the nth term formula in arithmetic progressions. This builds the foundation for advanced AP problems in Class 10 Maths.

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