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📘 Arithmetic Progressions Worksheet – Class 10 Chapter 5 Complete Practice Guide
Arithmetic Progressions (AP) are one of the most important topics in Class 10 Mathematics. This DigiSadhan online practice worksheet is designed to help students understand the pattern of an arithmetic progression and then apply the correct formula to solve numerical, conceptual and real-life questions. An arithmetic progression is a sequence of numbers in which the difference between consecutive terms remains constant. That fixed value is called the common difference, usually represented by d.
For example, 3, 7, 11, 15, 19, … is an AP because each term increases by 4. Here the first term is a = 3 and the common difference is d = 4. An AP can also decrease. For example, 20, 16, 12, 8, … has a common difference of −4. Recognising whether a sequence is an AP is the first skill students should master before moving to formulas.
1. Finding the Common Difference
The common difference is obtained by subtracting one term from the next: d = a₂ − a₁. The same difference must occur throughout the sequence. If the differences are unequal, the sequence is not an arithmetic progression. Always check at least two consecutive differences when a sequence is given.
2. Finding the nth Term
The nth-term formula is aₙ = a + (n − 1)d. Here, n represents the position of the required term. A common mistake is to use nd instead of (n − 1)d. For example, if a = 5, d = 3 and n = 10, the tenth term is 5 + 9 × 3 = 32. The formula is useful for finding a very distant term without listing every term.
3. Finding a Specific Term
Questions may give an AP and ask for its 8th, 15th, 25th or another term. Identify a, d and n first. Substitute these values carefully and simplify. When the common difference is negative, retain its sign throughout the calculation. Checking whether your result moves in the same direction as the sequence is a useful way to catch sign errors.
4. Finding the Sum of an AP
The sum of the first n terms is represented by Sₙ. When the first term and common difference are known, use Sₙ = n/2 [2a + (n − 1)d]. If the last term is known, the convenient form is Sₙ = n/2(a + l), where l is the last term. Students should choose the formula that matches the information supplied in the question.
5. Missing Terms and Relationships
Some worksheet problems provide an incomplete sequence such as 8, __, 20, 26. Since consecutive differences are equal, the missing value can be found from the surrounding terms. Other problems may give two terms of an AP and ask for the common difference or another term. In these questions, translate the information into the nth-term formula and solve systematically.
6. AP Word Problems
Arithmetic progressions occur in situations involving regular increases or decreases: seating arrangements, savings plans, monthly production, stacked objects, numbered rows and repeated distances. The key is to identify what represents the first term, what represents the common difference and what represents the number of terms. After modelling the situation as an AP, use the nth-term or sum formula as appropriate.
7. How to Use This Online Worksheet
Select the number of questions, question type and difficulty. Choose a timer if you want timed practice and switch sound on or off. Click Start New Test to generate a fresh worksheet. Questions are generated from varied numerical patterns rather than copied as one fixed list. Use Shuffle Whole Worksheet whenever you want a new arrangement and new values. Enter an answer and press Check Answer. Correct responses turn green and incorrect responses turn red. The answer remains hidden until the question has been checked.
8. Exam Preparation Tips
Begin with the definition of an AP and practise finding d. Then become comfortable with the nth-term formula. After that, practise sums and word problems. Write the known values before substituting them. Keep negative signs visible, especially for decreasing APs. For long questions, read the wording carefully and decide whether the problem asks for a term, number of terms or a sum. Finally, use the timer mode to practise working accurately under examination conditions.
9. Why Practice Matters
Repeated practice helps students recognise AP patterns quickly and select formulas confidently. This worksheet combines short numerical questions, conceptual checks, missing-term problems, sum questions and application-based problems. The instant feedback system lets students identify errors immediately, while the final score provides a simple measure of progress. Teachers and parents can also print the generated worksheet for offline revision.
Important: This is an independent DigiSadhan practice resource. Students should also use their prescribed textbook and classroom instruction for the complete syllabus and examination preparation.