Arithmetic Progressions rewards a student who knows just two formulas and uses them carefully: the nth term, a + (n − 1)d, and the sum of n terms, n/2 [2a + (n − 1)d]. With those, everything from “find the 10th term” to real-life savings and seating problems becomes a fill-in-the-values exercise. It is one of the calmest chapters to score well in — provided your child has practised spotting a, d and n cleanly.

This free printable worksheet has 12 questions from Bmathpro’s own question bank of 10,500+ validated maths questions — the same bank our enrolled students practise from. Every answer comes with a one-line explanation, so you can check your child’s method, not just the final answer.

Set aside 15–20 minutes, keep the answers hidden until the end, and let your child attempt every question — a wrong attempt tells you more than a skipped one.

What this worksheet covers

• The common difference and spotting an AP
• The nth term: a + (n − 1)d
• Finding which term equals a given value
• The sum of the first n terms
• Real-life AP word problems (savings, multiples, seating)

Maps to the CBSE Class 10 Arithmetic Progressions chapter (NCERT) and equivalent ICSE/State-board units.

Class 10 Arithmetic Progressions Worksheet — 12 Questions

Warm-up

1. What is the common difference of the AP 4, 11, 18, …? (Write your answer.)

2. Which sequence is an AP?
A. 1, 2, 4, 8  B. 1, 4, 9, 16  C. 3, 7, 11, 15  D. 2, 3, 5, 8

3. Find the 10th term of the arithmetic progression 2, 5, 8, … (Write your answer.)

Building up

4. The 4th term of an AP is 11 and the 7th is 20. Find the first term a. (Write your answer.)

5. Which term of the arithmetic progression 3, 7, 11, … is equal to 39? (Write your answer.)

6. Find the sum of the first 14 terms of the AP with a = 3, d = 2. (Write your answer.)

7. For the AP 7, 10, 13, 16, …, which statement is TRUE?
A. The common difference is 7  B. The nth term is 3n + 4, so the 20th term is 64  C. The 20th term is 60  D. The nth term is 3n + 7, so the 20th term is 67

8. Find the sum of the first 10 multiples of 3. (Write your answer.)

Challenge

9. A person saves ₹100 in the first month, ₹150 in the second, ₹200 in the third, and so on. How much (in ₹) does she save in the 12th month? (Write your answer.)

10. How many terms of the arithmetic progression 2, 4, 6, … add up to 90? (Write your answer.)

11. How many terms of the AP 24, 21, 18, … sum to 78? (Take the smaller positive value.) (Write your answer.)

12. Find the sum of the first 15 terms of the AP with a = 4, d = 3. (Write your answer.)

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Answer key with explanations

Show answers and explanations (parents — open this after your child finishes)

1. 7 — 11 − 4 = 7.
2. C. 3, 7, 11, 15 — constant difference of 4.
3. 29 — a = 2, d = 3; t₁₀ = 2 + 27 = 29.
4. 2 — 3d = 9 so d = 3; a = 11 − 9 = 2.
5. 10 — 3 + (n−1)4 = 39 → n = 10.
6. 224 — S₁₄ = 7(6 + 26) = 224.
7. B. nth term 3n + 4, 20th term 64 — a = 7, d = 3.
8. 165 — 3(1+2+…+10) = 3×55 = 165.
9. 650 — a = 100, d = 50; t₁₂ = 100 + 550 = 650.
10. 9 — n(n+1) = 90 → (n−9)(n+10), n = 9.
11. 4 — n² − 17n + 52 = (n−4)(n−13), smaller n = 4.
12. 375 — S₁₅ = 15/2 (8 + 42) = 375.

How to use this worksheet at home

• Keep it short and calm. 15–20 minutes beats an hour of pressure.
• Write a, d and n first. Ask your child to jot down the three values before touching a formula — most AP slips come from mixing them up.
• Praise the method, not the marks. (We deliberately don’t put marks on our worksheets.)

FAQs

Is this worksheet free to print?
Yes — free to use and print at home, no sign-up needed.

Which syllabus does it follow?
Standard Class 10 Arithmetic Progressions chapter — CBSE (NCERT), ICSE and State boards.

Which two AP formulas does my child really need?
Just two: the nth term a + (n − 1)d, and the sum n/2 [2a + (n − 1)d]. Almost every board question uses one of these — the skill is reading a, d and n from the question correctly. A free demo class shows how.

Where can my child get more practice like this?
Enrolled students get Math Gym, our paid practice app with 10,500+ questions — see our courses page.

Also practise: Real Numbers · Quadratic Equations · all Class 10 worksheets.

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