Class 11 Maths Chapter 8 Sequences and Series – Exercise 8.1 NCERT Solutions

Introduction

Exercise 8.1 introduces the concept of sequences and series, focusing on arithmetic progression (AP). You will learn how to identify APs, find common differences, and calculate terms using the general formula. This exercise builds the foundation for advanced series and summation techniques.

Key Concepts

1. Sequence: An ordered list of numbers following a specific rule.

2. Arithmetic Progression (AP): A sequence where each term after the first is obtained by adding a constant difference.

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

3. General Term of AP:

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

where $a$ = first term, $d$ = common difference, $n$ = term number.

NCERT Questions with Solutions (10)

Q1. Find 10th term of AP: 2, 7, 12, 17, …

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

Q2. Find 15th term of AP: 1, 4, 7, 10, …

$$a=1,d=3,a_{15}=1+(15-1)\cdot 3=43$$

Q3. Find 20th term of AP: 3, 8, 13, 18, …

$$a=3,d=5,a_{20}=3+(20-1)\cdot 5=98$$

Q4. Find 25th term of AP: 10, 20, 30, …

$$a=10,d=10,a_{25}=10+(25-1)\cdot 10=250$$

Q5. Find 12th term of AP: 7, 13, 19, …

$$a=7,d=6,a_{12}=7+(12-1)\cdot 6=73$$

Q6. Find 30th term of AP: 5, 9, 13, …

$$a=5,d=4,a_{30}=5+(30-1)\cdot 4=121$$

Q7. Find 18th term of AP: 4, 9, 14, …

$$a=4,d=5,a_{18}=4+(18-1)\cdot 5=89$$

Q8. Find 50th term of AP: 1, 6, 11, …

$$a=1,d=5,a_{50}=1+(50-1)\cdot 5=246$$

Q9. Find 22nd term of AP: 2, 5, 8, …

$$a=2,d=3,a_{22}=2+(22-1)\cdot 3=65$$

Q10. Find 40th term of AP: 3, 6, 9, …

$$a=3,d=3,a_{40}=3+(40-1)\cdot 3=120$$

FAQs (10)

1. What is a sequence? Ordered list of numbers.

2. What is arithmetic progression? Sequence with constant difference between terms.

3. What is general term of AP? $a_n=a+(n-1)d$.

4. What is first term? Denoted by $a$.

5. What is common difference? Difference between consecutive terms.

6. How to find nth term? Use formula $a_n=a+(n-1)d$.

7. Is AP always increasing? Not necessarily; depends on $d$.

8. Can AP be decreasing? Yes, if $d<0$.

9. Can AP have zero common difference? Yes, then all terms are equal.

10. Why is this exercise important? It builds foundation for sequences, series, and summation techniques.

Conclusion

Exercise 8.1 has 10 solved questions and 10 FAQs that strengthen your understanding of arithmetic progressions and general term formula. This builds the foundation for advanced series in Class 11 Maths.

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New Syllabus-Class 11 Maths Chapter 8 Sequences and Series – Exercise 8.1 NCERT Solutions