Worked example 1
Question: Find the 20th term and the sum of the first 20 terms of 5, 9, 13, …
Solution: a=5,d=4. a₂₀=5+19×4=81. S₂₀=20/2(5+81)=10×86=860.
What this chapter covers
Recognise a constant common difference, derive the nth term and sum formula, and use arithmetic progressions in everyday contexts.
Terms and common difference
An arithmetic progression (AP) is a sequence where the difference between consecutive terms is constant. Identify a, d and n carefully; d may be negative or zero. The last term is often written l.
Choosing a formula
Use the nth-term formula to locate a term. Use the sum formula when a question asks for the total of several terms. In word problems, first translate the starting amount and regular change into a and d.
Key formulae: aₙ=a+(n−1)d. Sₙ=n/2[2a+(n−1)d]=n/2(a+l).
Worked examples: CBSE question patterns
These are original practice questions modeled on common board-exam patterns; they are not reproduced past-paper questions.
Worked example 2
Question: A student saves ₹100 in week 1 and increases the saving by ₹20 each week. Find the total saved in 12 weeks.
Solution: a=100,d=20,n=12. S₁₂=12/2[200+11×20]=6×420=₹2,520.
Practical activity / investigation
Measure the heights of 6 steps in a staircase or use a staircase drawing. If each rise is equal, record cumulative height as a sequence and identify its first term, common difference and nth-term rule.
Record: Write the aim, materials, steps, observations and conclusion in your notebook. Follow teacher supervision for any classroom activity.
Quick practice with answers
Try each question before opening its solution.
Practice 1: Find the 15th term of 7, 4, 1, …
a=7,d=−3; a₁₅=7+14(−3)=−35.
Practice 2: How many terms of 3, 7, 11, … sum to 210?
Sₙ=n/2[6+4(n−1)]=n(2n+1)=210; 2n²+n−210=0=(2n+21)(n−10), so n=10.
Practice 3: Find the sum of the first 25 positive multiples of 6.
6+12+…+150 is an AP: S₂₅=25/2(6+150)=₹1,950.
Revision checklist
- Can I explain the key idea without memorising a worked solution?
- Have I selected the right formula and written units where needed?
- Can I show each algebraic or geometric step clearly?
- Can I check my answer by substitution, estimation or a diagram?
Aligned to the Class X Mathematics curriculum for 2026–27 and the NCERT Mathematics textbook. Always confirm any school-specific internal assessment with your teacher.