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Important Questions

Arithmetic Progressions

Punjab Board · Class 10 · Mathematics

Most important questions from Arithmetic Progressions for Punjab Board Class 10 Mathematics board exam 2026. MCQs, short answer, and long answer questions with marks.

45 questions25 flashcards5 concepts

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Illustrates the structure of an Arithmetic Progression (A.P.), showing the first term 'a' and common difference 'd', along with the general term formula.
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45 Questions·
multiple choice

Sample Questions

1multiple choice
1 marks

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.

2multiple choice
1 marks

If the pth term of an AP is q and the qth term is p (p ≠ q), what is the (p + q)th term?

3multiple choice
1 marks

The sum of four numbers in AP is 32 and the sum of their squares is 276. Find the largest of the four numbers.

Show answer

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.

4multiple choice
1 marks

The sum of n terms of an AP is 5n² - 3n. Which term of this AP is 152?

Show answer

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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Frequently Asked Questions

What are the important topics in Arithmetic Progressions for Punjab Board Class 10 Mathematics?
Key topics in Arithmetic Progressions include Arithmetic Progressions — Complete Chapter Overview, Flowchart showing the step-by-step process to identify if a sequence is an AP by checking if consecutive differences are constant, Mind map showing the structure and components of an AP. These are the concepts Punjab Board Class 10 examiners draw on most — study them first, then practise related questions.
How to score full marks in Arithmetic Progressions — Punjab Board Class 10 Mathematics?
Understand the core concepts first, then work through the 45 practice questions available for this chapter. Revise formulas and definitions regularly, and use flashcards for quick recall before the exam.
How many important questions are there in Arithmetic Progressions?
There are 45 practice questions available for Arithmetic Progressions. These cover multiple question types including MCQs, short answer, and long answer questions.

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