Exercise 5.1: Is it an AP? First term and common difference
What it tests. A list is an AP when the difference between each term and the one before it is the same every time. That fixed difference is \(d\); it can be positive, negative or zero.
NCERT Solutions for Class 10 Maths Chapter 5: Arithmetic Progressions
Recognising an AP, the nth term \(a_n = a + (n-1)d\), the sum \(S_n = \dfrac{n}{2}[2a + (n-1)d]\) and word problems built on them. Our own step-by-step solutions to Exercises 5.1 to 5.4, one page per exercise, set out for step marks.
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Chapter 5 exercises
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Exercise 5.2: The nth term
What it tests. \(a_n = a + (n-1)d\). Two facts about an AP give two equations in \(a\) and \(d\); "which term" questions solve for \(n\), which must be a positive whole number.
Exercise 5.3: Sum of the first n terms
What it tests. \(S_n = \dfrac{n}{2}[2a + (n-1)d]\), or \(S_n = \dfrac{n}{2}(a + l)\) when the last term \(l\) is known. Also \(a_n = S_n - S_{n-1}\).
Exercise 5.4: Optional: harder problems
What it tests. Harder uses of \(a_n\) and \(S_n\): inequalities for "first negative term", two conditions on two unknowns, and turning a physical set-up into an AP.
Done the NCERT exercises? The board paper asks more
Arithmetic Progressions has 39 original board-style questions (MCQ, assertion–reason, short and long answers, case studies) with step mark schemes, revision notes and a four-step Route to 95. Three sample questions are open to everyone; a free account opens the rest.
Also useful: free MCQs and case studies for Arithmetic Progressions · Class 10 formula sheet · official CBSE board and sample papers · our sample papers with marking scheme · the Route to 95 plan
Textbook: NCERT Mathematics Class 10 (rationalised edition, 2023-24 reprint onward), free from ncert.nic.in. Question statements are shortened to the minimum needed; the solutions and tips are our own. CBSE Math Revision is independent and not affiliated with NCERT or CBSE. Spotted a slip? Tell us and it goes in the corrections log.