CBSE • Class 10 • Mathematics • Chapter 5 (Arithmetic Progressions) • Exercise 5.1

Exercise 5.1: Arithmetic Progressions — NCERT Solutions

Identifying arithmetic progressions and writing the common difference.

Aligned to the latest NCERT 2024-25 edition • 4 questions in this exercise • Free plan, no credit card

Open this exercise in the AI tutorBack to Chapter 5

What this exercise covers

First termCommon differencePattern check

Step-by-step solutions — Exercise 5.1

3 solved questions • Each solution includes a Socratic hint, full working and a common-mistake callout • Last reviewed 2026-09-03

Exercise 5.1 Q1 • 2 marks

Check whether the list of numbers 3,7,11,15,…3, 7, 11, 15, \dots forms an arithmetic progression. If it does, write its common difference.
Hint (Socratic — try this first)▾
What do you get when you subtract each term from the one that follows it?
Step-by-step solution▾

To be an AP, the difference between consecutive terms must be constant.

  • a2−a1=7−3=4a_2 - a_1 = 7 - 3 = 4
  • a3−a2=11−7=4a_3 - a_2 = 11 - 7 = 4
  • a4−a3=15−11=4a_4 - a_3 = 15 - 11 = 4

Since the difference is the same each time, the list is an AP with common difference d=4d = 4.

Common mistake:
Computing the difference in the wrong order (earlier term minus later term) and getting −4-4, or checking only one pair of terms.
Open this question in the AI tutor →

Exercise 5.1 Q2 • 3 marks

The fare of a taxi is ₹15 for the first kilometre and ₹8 for each additional kilometre. Write the sequence of total fares (in ₹) for 1, 2, 3, 4 km and state whether it forms an AP.
Hint (Socratic — try this first)▾
How much is added to the fare for every extra kilometre travelled?
Step-by-step solution▾

Fare for 1 km =15= 15.

Each additional km adds ₹8:

  • 2 km: 15+8=2315 + 8 = 23
  • 3 km: 23+8=3123 + 8 = 31
  • 4 km: 31+8=3931 + 8 = 39

Sequence: 15,23,31,39,…15, 23, 31, 39, \dots

Differences: 23−15=823-15 = 8, 31−23=831-23 = 8, 39−31=839-31 = 8.

Since the common difference is constant, the fares form an AP with a=15a = 15 and d=8d = 8.

Common mistake:
Taking the first term as ₹8 instead of ₹15, forgetting that the fixed ₹15 covers the first kilometre.
Open this question in the AI tutor →

Exercise 5.1 Q3 • 2 marks

For the AP −5,−1,3,7,…-5, -1, 3, 7, \dots, write the first term aa and the common difference dd.
Hint (Socratic — try this first)▾
Which term is aa, and what constant is being added each step?
Step-by-step solution▾

The first term is the very first number: a=−5a = -5

The common difference is any term minus the previous one: d=−1−(−5)=−1+5=4d = -1 - (-5) = -1 + 5 = 4

So a=−5a = -5 and d=4d = 4.

Common mistake:
Mishandling the negative sign, e.g. writing −1−(−5)=−6-1 - (-5) = -6 instead of 44.
Open this question in the AI tutor →

How to approach Exercise 5.1

  1. Re-read the chapter summary first. Open Arithmetic Progressions and refresh the key concepts: First term, Common difference, nth term, Sum of n terms.
  2. Try each problem yourself before opening the solution. Ten focused minutes per problem usually beats reading two finished solutions.
  3. Use Guru AI for the questions you get stuck on. The Socratic AI tutor walks you through it with hints instead of dictating the answer.
  4. Mark the questions you got wrong and revisit them after 24 hours — the spacing is what locks the method into long-term memory.

All exercises in Arithmetic Progressions

  1. Exercise 5.1 — Identifying arithmetic progressions and writing the common difference.
  2. Exercise 5.2 — nth term of an AP — applying aₙ = a + (n − 1)d in direct and word problems.
  3. Exercise 5.3 — Sum of first n terms — Sₙ = n/2 [2a + (n − 1)d].
  4. Exercise 5.4 — Mixed AP problems combining nth term and sum, including pattern problems.

Exercise 5.2 →

nth term of an AP — applying aₙ = a + (n − 1)d in direct and word problems.

Solve Exercise 5.1 with AI guidance

Free plan. No credit card. Works on any device.

Start Free