Class 10 Maths Chapter 5 Arithmetic Progressions – Exercise 5.1 NCERT Solutions

Introduction

Exercise 5.1 introduces the concept of Arithmetic Progression (AP). An AP is a sequence of numbers in which each term after the first is obtained by adding a fixed number, called the common difference (d), to the preceding term. This exercise focuses on identifying APs and finding their common difference.

Formula Used

• General Form of AP:

$$a,a+d,a+2d,a+3d,\dots$$

• nth Term of AP:

$$a_n=a+(n-1)d$$

NCERT Questions with Solutions (10)

Q1. Check whether 2, 4, 6, 8, … is an AP.

Solution: Common difference $d=4-2=2$. Yes, it is an AP.

Q2. Check whether 1, 3, 9, 27, … is an AP.

Solution: Differences: $3-1=2$, $9-3=6$. Not equal. Not an AP.

Q3. Check whether -1, -3, -5, -7, … is an AP.

Solution: Common difference $d=-3-(-1)=-2$. Yes, it is an AP.

Q4. Check whether 10, 7, 4, 1, … is an AP.

Solution: Common difference $d=7-10=-3$. Yes, it is an AP.

Q5. Check whether 5, 10, 15, 20, … is an AP.

Solution: Common difference $d=10-5=5$. Yes, it is an AP.

Q6. Check whether 2, 5, 10, 17, … is an AP.

Solution: Differences: $5-2=3$, $10-5=5$. Not equal. Not an AP.

Q7. Check whether 3, 6, 12, 24, … is an AP.

Solution: Differences: $6-3=3$, $12-6=6$. Not equal. Not an AP.

Q8. Check whether 1, 2, 3, 4, … is an AP.

Solution: Common difference $d=2-1=1$. Yes, it is an AP.

Q9. Check whether 0, 5, 10, 15, … is an AP.

Solution: Common difference $d=5-0=5$. Yes, it is an AP.

Q10. Check whether 7, 14, 21, 28, … is an AP.

Solution: Common difference $d=14-7=7$. Yes, it is an AP.

FAQs (10 from NCERT)

1. Q: What is an arithmetic progression (AP)? A: A sequence where each term differs from the previous by a constant.

2. Q: What is the common difference? A: The fixed number added to each term to get the next.

3. Q: What is the first term of an AP? A: The starting number, denoted by $a$.

4. Q: What is the nth term formula? A: $a_n=a+(n-1)d$.

5. Q: Can AP have negative common difference? A: Yes, then terms decrease.

6. Q: Can AP have zero common difference? A: Yes, then all terms are equal.

7. Q: Is 2, 4, 8, 16 an AP? A: No, it is a geometric progression.

8. Q: What is a finite AP? A: An AP with limited terms.

9. Q: What is an infinite AP? A: An AP that continues indefinitely.

10. Q: Why is this exercise important? A: It builds the foundation for AP problems in higher classes.

Conclusion

Exercise 5.1 has 10 solved questions and 10 FAQs that strengthen your understanding of arithmetic progressions and their common difference. This builds the foundation for solving AP problems in Class 10 Maths.

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