Class 10 / Maths
Class 10 Maths Arithmetic Progressions Worksheet
Practice nth term, common difference, sum of terms, and word problems on arithmetic progressions.
advanced45 minutesAnswer key included
Learning objective
Practise identifying APs, finding nth terms, calculating sums, and applying AP formulas to word problems.
Questions
- Check whether 2, 5, 8, 11, ... is an AP. If yes, find d.
- Find the 15th term of 4, 9, 14, 19, ...
- Find the 30th term of the AP 10, 7, 4, 1, ...
- Which term of 6, 11, 16, ... is 101?
- Find the sum of first 20 terms of 3, 6, 9, 12, ...
- Find the sum of first 15 terms of 8, 13, 18, ...
- The first term of an AP is 12 and common difference is 5. Find the 25th term.
- If a = 7, d = 3, and a_n = 70, find n.
- Find the sum of all two-digit numbers divisible by 3.
- A student saves Rs. 20 in the first week and increases savings by Rs. 5 every week. How much will the student save in 12 weeks?
Answer key
Show suggested answers
- Yes. The common difference is 5 - 2 = 3.
- Here a = 4, d = 5. a15 = 4 + 14 x 5 = 74.
- Here a = 10, d = -3. a30 = 10 + 29 x (-3) = -77.
- 101 = 6 + (n - 1)5, so 95 = 5(n - 1), n - 1 = 19, and n = 20.
- 3, 6, 9, ... has a = 3, d = 3. S20 = 20/2[2 x 3 + 19 x 3] = 630.
- 8, 13, 18, ... has a = 8, d = 5. S15 = 15/2[16 + 70] = 645.
- a25 = 12 + 24 x 5 = 132.
- 70 = 7 + (n - 1)3, so 63 = 3(n - 1), n - 1 = 21, and n = 22.
- Two-digit multiples of 3 are 12, 15, ..., 99. There are 30 terms. Sum = 30/2(12 + 99) = 1665.
- Savings form an AP with a = 20, d = 5, n = 12. S12 = 12/2[40 + 55] = Rs. 570.
How to use this worksheet
Students can solve the questions independently first, then review errors with a parent or teacher. Teachers can use it as a short class activity, homework sheet, or revision check.
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