CBSE Class 10 · Boards 2027 · NCERT 2026-27 syllabus
NCERT Solutions Class 10 Maths Chapter 5 Arithmetic Progressions
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Boards begin February 2027
Pre-boards are in December
Arithmetic Progressions is in Algebra, which carries 20 of the 80 marks in the 2026-27 CBSE Maths paper
A contract on a construction job specifies a penalty for delay of completion as ₹200 for the first day, ₹250 for the second day, ₹300 for the third day, etc., the penalty for each succeeding day being ₹50 more than for the preceding day. How much money must the contractor pay as penalty if the work is delayed by 30 days?
Step 1Daily penalties form an AP: 200, 250, 300, …, with a = 200 and d = 50.
Step-by-step solution
Daily penalties form an AP: 200, 250, 300, …, with a = 200 and d = 50.
A manufacturer of TV sets produced 600 sets in the third year and 700 sets in the seventh year. Assuming that the production increases uniformly by a fixed number every year, find (i) the production in the 1st year, (ii) the production in the 10th year, (iii) the total production in the first 7 years.
Step 1Let aₙ denote production in the nth year. a₃ = 600 and a₇ = 700.
Step-by-step solution
Let aₙ denote production in the nth year. a₃ = 600 and a₇ = 700.
a + 2d = 600 and a + 6d = 700. Subtract: 4d = 100 ⇒ d = 25.
(i) a = 600 − 2 × 25 = 550. Production in year 1 = 550 sets.
CBSE board pattern: Assertion-Reason and case-based questions
Written in the CBSE board format. These are not numbered NCERT/Exemplar questions; some case studies are built on textbook problems. Neither NCERT book has Assertion-Reason questions: they, and case-based questions, are a CBSE board-paper format, here on this chapter's 2026-27 syllabus, with solutions by LazyTopper.
CBSE board pattern · Assertion-Reason1 mark
Assertion (A): The list of numbers −10, −6, −2, 2, … is an AP with common difference 4.
Reason (R): A list of numbers is an AP if aₖ₊₁ − aₖ is the same constant for every k.
Step 1Check differences: −6 − (−10) = 4, −2 − (−6) = 4, 2 − (−2) = 4. All equal, so A is true.
Step-by-step solution
Check differences: −6 − (−10) = 4, −2 − (−6) = 4, 2 − (−2) = 4. All equal, so A is true.
R is the standard definition of an AP — true.
We used R to verify A, so R is the correct explanation.
200 logs are stacked so that 20 logs are in the bottom row, 19 in the next row, 18 in the next, and so on.
(i) Write the AP formed by the number of logs in successive rows.
(ii) How many rows are needed to stack 200 logs?
(iii) How many logs are in the top row?
(iv) What is the common difference?
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Questions from the NCERT Class 10 Mathematics textbook (the CBSE board-pattern section is in the board format, not numbered book questions); the solutions are written by LazyTopper. LazyTopper is an independent platform and is not affiliated with CBSE or NCERT.