NCERT Solutions Class 10 Maths Chapter 5 — Arithmetic Progressions#

Chapter 5 introduces Arithmetic Progressions (AP) — sequences where each term differs from the previous by a constant (common difference). You will find the nth term and the sum of the first n terms of an AP, and solve a wide range of real-life problems involving AP.

exercise 5.1 exercise 5.2 exercise 5.3 exercise 5.4

Exercises#

  • Exercise 5.1 — Introduction to AP, finding the nth term (4 questions)
  • Exercise 5.2 — Sum of first n terms of an AP (20 questions)
  • Exercise 5.3 — Word problems on AP (20 questions)
  • Exercise 5.4 — Advanced word problems on AP (5 questions)

What you will learn#

  • Recognise an arithmetic progression and find its common difference.
  • Find the nth term, and which term of an AP is a given number.
  • Find the sum of the first n terms of an AP.
  • Apply APs to savings, instalments, prizes and rows of seats.

Key formulas and results#

  • nth term: $a_n = a + (n - 1)d$.
  • Sum of the first $n$ terms: $S_n = \dfrac{n}{2}[2a + (n - 1)d]$.
  • When the last term $l$ is known: $S_n = \dfrac{n}{2}(a + l)$.

Read and revise#

Frequently asked questions#

How many exercises are in Class 10 Maths Chapter 5?
Four: Exercise 5.1 (4 questions), Exercise 5.2 (20 questions), Exercise 5.3 (20 questions) and Exercise 5.4 (5 questions) — 49 questions in all, each solved step by step here.
How do you check whether a list of numbers is an AP?
Subtract each term from the next one. If the difference is the same every time, the list is an AP, and that difference is its common difference d.

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