NCERT Mathematics, Class 10, textbook pages 49–72

How to help your child with Class 10 Maths Chapter 5, Arithmetic Progressions, at home

nth term and sum of an AP, explained for parents: a 45-minute study session, a quick challenge, a 5-day plan and the mistakes to watch for.

aₙ = a + (n − 1)dSₙ = n/2 [2a + (n − 1)d]3, 7, 11, … a₁₀ = 39

NCERT Class 10 Maths Chapter 5 Arithmetic Progressions: what it teaches

Your teen identifies APs in everyday situations, finds the nth term aₙ = a + (n − 1)d and the sum Sₙ = n/2 [2a + (n − 1)d], and solves savings, salary and seating problems.

Why it matters later. APs lead to sequences and series (Class 11) and finance maths.

See it: this chapter in pictures

₹20,000 + ₹1,500 each yearyear 10: 20000 + 9 × 1500= ₹33,500
Real-life APs.
1 + 3 + 5 + … (50 terms)= 50/2 × (1 + 99)= 2500
Sum = n/2 × (first + last).
3 + 7 + 11 + … = 210n(2n + 1) = 210n = 10
Leads to a quadratic in n.

You need

  • a calculator
  • examples like salaries with yearly increments

Tonight’s 45 minutes

  1. Salary ₹20,000 rising by ₹1,500 a year: what in year 10? (₹33,500)
  2. Sum of the first 50 odd numbers (2500).
  3. How many terms of 3, 7, 11… make 210? (10)
  4. Find the middle term of an AP with 21 terms.

Words to use

  • AP
  • first term
  • common difference
  • nth term
  • sum of n terms

Watch for

  • Using n instead of n − 1. Test the formula with n = 1.
  • Mixing aₙ and Sₙ. Ask: does the question want one term or a total?

What it sounds like at home

A short example of the conversation. Your words will differ; the questions are what matter.

You3, 7, 11… how many terms make 210?

Your childn/2(6 + 4(n − 1)) = 210 → n = 10.

A game for this week: Savings planner

  1. Choose a starting saving and monthly increase.
  2. Predict the total after a year.
  3. Calculate with the sum formula.
  4. Closest prediction wins.

A 5-day plan, 45 minutes a day

  1. Day 1Explain-back.
  2. Day 2Worked examples.
  3. Day 3Practice set.
  4. Day 4Real-life problem.
  5. Day 5Mixed quiz.

Everyday moments to practise

  • Salary increments.
  • EMI and savings.
  • Seating in theatres.
  • Stacked logs.

Quick check

Ask these at the end of the week. Tap to see the answer.

10th term of 3, 7, 11…?

39.

Sum of first 50 odd numbers?

2500.

Year-10 salary in the example?

₹33,500.

Ready for the next chapter when your child…

  • Uses nth-term and sum formulas.
  • Solves word problems.
  • Checks answers for sense.

Activities, wording and illustrations are Mathify Kids’ own, following the topics of NCERT’s Mathematics (Class 10). See the full Class 10 parent guide for every chapter.

Questions parents ask

What is an AP?

A sequence with constant difference.

Formula for sum?

Sₙ = n/2 [2a + (n − 1)d] or n/2 (a + l).

How to find how many terms?

Set Sₙ equal to the total and solve the quadratic in n.