‘रचना-प्रयोग’ का मुख्य उद्देश्य क्या है?

व्याकरण का व्यावहारिक प्रयोग सिखाना

‘द्वितीयः’ किस प्रकार की संख्या है?

क्रमवाचक (दूसरा)

Find the 10th term of the AP: 2, 5, 8, …

\(a = 2,\ d = 3\), so \(a_{10} = 2 + 9 \times 3 = 29\).

Write the formula for the sum of the first \(n\) terms of an AP.

\(S_n = \dfrac{n}{2}\,[2a + (n - 1)d]\), or \(\dfrac{n}{2}(a + l)\) where \(l\) is the last term.

Write the formula for the nth term of an AP.

\(a_n = a + (n - 1)d\), where \(a\) is the first term and \(d\) is the common difference.

Write the formula for the sum of the first n terms of an AP.

\(S_n = \dfrac{n}{2}\,[2a + (n - 1)d]\), or \(S_n = \dfrac{n}{2}(a + l)\) when the last term \(l\) is known.

Find the common difference and the 10th term of the AP 3, 7, 11, …

\(d = 7 - 3 = 4\); \(a_{10} = 3 + 9 \times 4 = 39\).

How many two-digit numbers are divisible by 3?

They form the AP 12, 15, …, 99; with \(a = 12,\ d = 3,\ l = 99\): \(n = (99 - 12)/3 + 1 = 30\) numbers.

Find the sum of the first 20 terms of the AP 2, 5, 8, …

\(a = 2,\ d = 3\): \(S_{20} = \dfrac{20}{2}[2(2) + 19(3)] = 10(4 + 57) = 610\).

Which term of the AP 5, 9, 13, … is 81?

\(a_n = 5 + (n - 1)4 = 81 \Rightarrow (n - 1)4 = 76 \Rightarrow n = 20\); so 81 is the 20th term.

Is 0 a term of the AP 31, 28, 25, …? Explain.

\(a = 31,\ d = -3\): \(a_n = 31 - 3(n - 1) = 0\) gives \(n = 34/3\), which is not a whole number, so 0 is not a term.

CBSE · Board years

CBSE Class 10 — Notes, Chapters & Practice Quizzes

Your Class 10 year, organised — chapter notes, board-style questions and a practice quiz for every chapter.

7 subjects 143 chapters 149 practice quizzes NCERT syllabus

126 quiz attempts so far Dual AI-verified questions 10 quizzes free, then ₹9 per quiz

Notice Board

10 questions · instant score · weak-chapter diagnosis

01 Choose a chapter02 Revise key ideas03 Test recall

Students preparing for CBSE Class 10 Board Examination

View all

Formula of the day

Maths · Quadratic equations · 9 formulae in the cheatsheet

Trap of the day

sin²θ means (sinθ)², not sin(θ²). A pure notation trap that changes the value.

IIT Guidance Practice QuizFind weak topics English Health and Physical Education Hindi Mathematics Sanskrit Science PYQ PapersSolve official papers Mock TestsRehearse exam day DiscussionAsk the community

Mathematics · 14 chapters

Summary, key terms, extra questions with answers and a practice quiz with AI diagnosis for each.

Chapter 5: Arithmetic ProgressionsClass 10 Mathematics — summary, notes, extra questions & NCERT solutions

Q: What is an arithmetic progression (AP)?

A list of numbers in which each term is obtained by adding a fixed number, the common difference d, to the preceding term.

Try one from this chapter

The common difference of the AP 2, 5, 8, 11, … is:

Summary

An arithmetic progression (AP) is a list of numbers in which each term is obtained by adding a fixed number, the common difference, to the previous term. The chapter derives two central formulae: the nth term \(a_n = a + (n-1)d\), and the sum of the first \(n\) terms \(S_n = \dfrac{n}{2}\,[2a + (n-1)d]\) (equivalently \(\dfrac{n}{2}(a + l)\) when the last term \(l\) is known). These let students find any term, count terms, and add long sequences quickly. APs model many real situations such as savings, salaries and seating arrangements.

nth term of an APSum of first n termsApplications of AP

Key terms

Arithmetic progression

A sequence with a constant difference between consecutive terms.

Common difference (d)

The fixed amount added to get the next term.

nth term

\(a_n = a + (n - 1)d\).

Sum of n terms

\(S_n = \dfrac{n}{2}\,[2a + (n - 1)d]\).

Extra questions & answers

EXERCISE 5.1

EXERCISE 5.2

EXERCISE 5.3

EXERCISE 5.4 (Optional)*

Explore interactively

nth term and sum of an AP

adn

2, 5, 8, 11, 14, …

nth term aₙ

Sum Sₙ

155

Key-term flashcards

Flip cards · mark known · keyboard ← → and Space

4 cards

Term1 / 4

Arithmetic progression

Tap to reveal

Meaning1 / 4

A sequence with a constant difference between consecutive terms.

Tap to flip back

Tap card to flip

Keyboard: ← → to move · Space to flip

Practice quiz · Arithmetic Progressions

Score on this chapter, climb the leaderboard, and get an AI diagnosis of your mistakes.

Dual AI-verified questions Real exam pattern 1 free quiz, first unlock ₹1, then ₹9

Arithmetic Progressions

Start here

Maths 10 Qs · ~10 min

Instant score, answer review and weak-topic diagnosis

7.5/10avg score

8/10best

Your Class 10 board-year rhythm

1
A little every day
Chapter notes and one quiz a day beat a month of last-minute cramming.
2
Board-pattern practice
Extra questions with answers and quizzes asked the way the board asks them.
3
Results you can show off
Scorecards, leaderboards and AI analysis of every attempt.