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Class 10 Arithmetic Progressions — practice questions with answers

Algebra — Sequences · 5 sample questions from the school syllabus. Try each one, then open the answer and the worked solution.

1. Find the 10th term of AP 3, 8, 13, 18, ….
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Answer: A) 48
a = 3, d = 5. a₁₀ = 3 + 9·5 = 48.
2. A man saves Rs 200 in the first month and increases his savings by Rs 50 each month. How much does he save in the 10th month?
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Answer: D) 650
a = 200, d = 50. a₁₀ = 200 + 9(50) = 200 + 450 = 650 rupees.
3. In a school stadium, the first row has 20 seats and each successive row has 2 more seats than the row in front. How many seats are there in the 15th row?
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Answer: D) 48
a = 20, d = 2. a₁₅ = 20 + 14(2) = 20 + 28 = 48 seats.
4. 200 logs are stacked so that the bottom row holds 20 logs, the row above it 19, the next 18, and so on. In how many rows are the 200 logs placed?
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Answer: B) 16
a = 20, d = -1. → → (n - 16)(n - 25) = 0. Although n = 25 satisfies the equation, the 21st row would already contain 0 logs, so it is rejected. There are 16 rows, the top one holding 5 logs.
5. The first term of an AP is 3 and the sum of its first 9 terms is 171. Find its common difference.
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Answer: C) 4
→ 6 + 8d = 38 → 8d = 32 → d = 4. Check with the AP 3, 7, 11, …: .
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