Arithmetic Progressions — Important Questions
Punjab Board · Class 10 · Mathematics
45 important questions from Arithmetic Progressions for Punjab Board Class 10 Mathematics, with answers. Includes multiple choice questions.
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Important Questions from Arithmetic Progressions
In an AP, the sum of first 10 terms is -150 and the sum of its next 10 terms is -550. Find the first term of the AP.
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3
Step 1: S₁₀ = -150 → 5[2a + 9d] = -150 → 2a + 9d = -30 ... (i) Step 2: Sum of next 10 terms = S₂₀ - S₁₀ = -550 → S₂₀ = -700. Step 3: S₂₀ = -700 → 10[2a + 19d] = -700 → 2a + 19d = -70 ... (ii) Step 4: Subtract (i) from (ii): 10d = -40 → d = -4. Substitute in (i): 2a + 9(-4) = -30 → 2a = 6 → a = 3. The first term is 3.
If the pth term of an AP is q and the qth term is p (p ≠ q), what is the (p + q)th term?
The sum of four numbers in AP is 32 and the sum of their squares is 276. Find the largest of the four numbers.
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11
Step 1: Let four numbers in AP be (a-3d), (a-d), (a+d), (a+3d) with common difference 2d. Step 2: Sum = 4a = 32 → a = 8. Step 3: Sum of squares: (a-3d)² + (a-d)² + (a+d)² + (a+3d)² = 276. Step 4: = 4a² + 20d² = 276 → 4(64) + 20d² = 276 → 20d² = 20 → d² = 1 → d = 1. Step 5: Numbers are 5, 7, 9, 11. Largest = 11.
The sum of n terms of an AP is 5n² - 3n. Which term of this AP is 152?
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16th
Step 1: Find general term: aₙ = Sₙ - Sₙ₋₁ = (5n² - 3n) - [5(n-1)² - 3(n-1)]. Step 2: = 5n² - 3n - [5n² - 10n + 5 - 3n + 3] = 5n² - 3n - 5n² + 13n - 8 = 10n - 8. Step 3: Set aₙ = 152: 10n - 8 = 152 → 10n = 160 → n = 16. Step 4: Verify: a₁₆ = 10(16) - 8 = 160 - 8 = 152. ✓ The 16th term is 152.
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