Textbook chapter 5
Recognise a sequence with a constant change, locate a distant term without listing every term, and add many terms efficiently.
Textbook exercise solutions
- Exercise 5.1 — 4 question groups
- Exercise 5.2 — 20 question groups
- Exercise 5.3 — 20 question groups
- Exercise 5.4 — 5 question groups
Videos, notes and tests
English · Session 2026–27 · NCERT-aligned study guide
Chapter overview
Recognise a sequence with a constant change, locate a distant term without listing every term, and add many terms efficiently.
Before you begin: Number patterns, substitution and simple equations.
Key concepts · Solved examples · Practice · Mind map · Timed chapter test
Learn the key concepts
Recognising an AP
Consecutive differences must be equal. The common difference d may be positive, negative or zero. A sequence such as 2,4,8 is not an AP because its differences change.
The nth term
Starting at a, reaching term n involves n−1 equal steps, not n steps. To test whether a number belongs to an AP, solve for n and require a positive integer.
Summing and modelling
Pair the first and last terms: every pair has the same sum. This produces the sum formula. In savings problems, distinguish the amount saved in the nth week from the total saved through n weeks.
Formula and result checklist
- aₙ=a+(n−1)d.
- Sₙ=n[2a+(n−1)d]/2 = n(a+l)/2, where l=aₙ.
Solved examples
Example 1
Find the 20th term of 7,11,15,…
a=7,d=4. a₂₀=7+19×4=83.
Example 2
Find the sum of the first 15 terms of 3,8,13,…
a=3,d=5. S₁₅=(15/2)[6+14×5]=(15/2)×76=570.
Example 3
A student saves ₹40 in week 1 and ₹10 more each successive week. Find the total through week 12.
The deposits form an AP with a=40,d=10. The week-12 deposit is 40+11×10=150. Total=(12/2)(40+150)=₹1140.
Try it yourself
Work on paper before opening each answer. Show the reasoning and include units when needed.
1. Find the 12th term of 20,17,14,…
Check answer 1
20+11(−3)=−13.
2. Is 101 a term of 5,11,17,…?
Check answer 2
Yes; 5+(n−1)6=101 gives n=17.
3. Find 1+2+…+50.
Check answer 3
50×51/2=1275.
Common mistakes to avoid
- Use n−1 in the nth-term formula.
- Do not confuse aₙ with Sₙ.
Chapter mind map
View this chapter in the Mind Maps library · Open full-size image
Check your understanding
Take the 6-question, 10-minute chapter practice test. Each correct answer earns 1 mark; there is no negative marking. See explanations after submission.
Start chapter 5 practice test →
Continue learning
Read the corresponding chapter in the official NCERT textbook, then complete its exercises on paper. These NSL explanations and original practice questions support your textbook study; they are not an exercise-by-exercise solution manual.
Official CBSE syllabus 2026–27 · All chapters · Previous chapter · Next chapter
Check what you have learned
Finished the topics? Practise with the free chapter test.
Start free test