NCERT  ·  Mathematics  ·  Class X  ·  Ch.5

Arithmetic Progressions
MCQ Master Series

AP Basics · nth Term · Sum of n Terms · Term Number & Word Problems

🎯 50 Questions
⏱ 45 min Suggested
📊 3 Difficulty Tiers
🗂 5 Topics
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Question Intelligence

Quiz Analytics

A data-driven breakdown of all 50 questions by difficulty, exam origin and topic distribution.

📈 Distribution Overview

50
Total Questions
Formula & Concept Check
30
Applying Formulas to Find Term / n
14
Algebraic / Sn-based Reasoning
6

🗂 Topic Coverage

Definition & Identification of AP
16%
nth Term & Common Difference
34%
Sum of n Terms (Sn)
30%
Number of Terms & Term from End
12%
Sn as Function of n (Quadratic)
8%
30
Formula & Concept Check
14
Applying Formulas to Find Term / n
6
Algebraic / Sn-based Reasoning
Conceptual Framework

Key Concept Highlights

6 foundational pillars that power every question in this quiz. Understand these, and the answers follow naturally.

📏
Basics of Arithmetic Progression
An arithmetic progression is a sequence where the difference between consecutive terms is constant, called the common difference.
🔢
nth Term of an AP
If the first term is a and the common difference is d, then the nth term of an AP is given by a_{n} = a + (n-1)d.
➕
Sum of First n Terms
The sum of the first n terms of an AP with first term a and common difference d is S_{n} = \frac{n}{2}[2a + (n-1)d], which is used frequently in exam problems.
📐
Finding Term Position & Number of Terms
To find which term has a given value or how many terms an AP has up to a certain last term, we solve a + (n-1)d = l or use the sum formula as an equation in n.
📊
AP from Sum Formula S_n
When S_{n} is given as a quadratic expression in n, the first term is S_{1} and the common difference comes from subtracting successive sums, i.e., a_{n} = S_{n} - S_{n-1}.
🔄
Terms from the End & Means
A term from the end of a finite AP can be treated as a term of another AP starting from the last term backward, and the arithmetic mean of two numbers is the middle term of the AP formed by them.
Pedagogical Value

Why MCQs Matter

Multiple-choice questions are not mere guessing games — they are the sharpest diagnostic tool available to a competitive exam aspirant.

  • Force precise recall — vague conceptual understanding gets exposed immediately
  • Train elimination logic, a critical skill in JEE where partial knowledge suffices
  • Mirror the exact format of CBSE Board objective sections and JEE Main Paper 1
  • Build exam temperament: decisive, timed, confident decision-making
  • Reveal misconceptions that long-answer formats often mask
  • Provide instant feedback loops — every wrong answer is a targeted study pointer
~10–12%

of Class 10 Maths Algebra weightage under “Arithmetic Progressions” in school exams, periodic tests and CBSE board papers.

Quick Reference

Important Formula Capsules

6 must-memorise equations that surface repeatedly across CBSE and JEE papers.

nth Term of AP
\[ a_{n} = a + (n-1)d \]
Sum of First n Terms
\[ S_{n} = \dfrac{n}{2}[2a + (n-1)d] \]
nth Term from the End
\[ T_{n\text{ from end}} = l - (n-1)d \text{ where } l \text{ is last term} \]
Arithmetic Mean of Two Terms
\[ \text{If } a, b, c \text{ are in AP then } b = \dfrac{a + c}{2}. \]
Term from S_n Expression
\[ a_{n} = S_{n} - S_{n-1} \]
Number of Terms (Given Last)
\[ \text{If last term } l = a + (n-1)d,\\\text{then } n = \dfrac{l-a}{d} + 1. \]
Learning Outcomes

What You Will Learn

By completing this quiz set you will have exercised all the following competencies.

01 Recognise whether a given sequence is an arithmetic progression and identify its first term and common difference.
02 Use the nth-term formula a_{n} = a + (n-1)d to compute specific terms and to find the position of a given term in an AP.
03 Apply the sum formula S_{n} = \frac{n}{2}[2a + (n-1)d] to evaluate sums of the first n terms and to solve for n when the sum is known.
04 Determine the number of terms in a finite AP when the first term, common difference and last term are given.
05 Work with APs defined by S_{n}, using S_{n} - S_{n-1} to recover a_{n}, and then reading off the first term and common difference.
06 Solve exam-style problems involving arithmetic means, terms from the end of an AP and comparisons between two different APs.
07 Translate worded statements about progressions into algebraic equations using the standard AP formulas confidently.
Exam Preparation

Strategy & Preparation Tips

5 evidence-based strategies to maximise your score in CBSE Boards and JEE.

Step 01
Fix the Core Formulas
Memorise a_{n} = a + (n-1)d and S_{n} = n/2[2a + (n-1)d] perfectly; most of your 50 MCQs reduce to plugging into these two relationships.
Step 02
Mark Given & Required Clearly
For each question, quickly mark what is given (a, d, n, l, S_{n}) and circle what is asked (term, sum or n) so you choose the right formula without confusion.
Step 03
Use Equation in n Smartly
When you have “which term is 83?” type questions, set up a + (n-1)d = value and solve the linear equation in n instead of guessing terms.
Step 04
Handle S_n Questions Systematically
If S_{n} is given as a formula, first compute S_{1} and S_{2}, find a_{1} and a_{2}, then deduce the common difference before attempting the asked term.
Step 05
Check Reasonableness of Answers
After finding n, quickly see if the term index and term value fit the pattern of increasing or decreasing AP so you can eliminate impossible options.

Ready to Test Your Mastery?

50 questions  ·  Elapsed timer  ·  Instant scored results

⚡ Begin Arithmetic Progressions Quiz
🎯 Knowledge Check

Maths — ARITHMETIC PROGRESSIONS

50 Questions Class 10 MCQs
1
Which of the following is an arithmetic progression (AP)?
2
The common difference of the AP \(10, 7, 4, 1, \ldots\) is:
3
The \(n\)th term of an AP with first term \(a\) and common difference \(d\) is:
4
For the AP \(5, 10, 15, \ldots\), the 7th term is:
5
If three numbers \(a, b, c\) are in AP, then:
6
The 10th term of the AP \(3, 6, 9, 12, \ldots\) is:
7
Which of the following sequences is NOT an AP?
8
In an AP, the 3rd term is \(12\) and the 7th term is \(28\). The common difference is:
9
The sum of the first \(n\) terms of an AP with first term \(a\) and common difference \(d\) is:
10
In an AP, if \(a_1 = 5\) and \(a_4 = 17\), then the common difference is:
11
Which of the following is an AP with common difference \(-3\)?
12
The 5th term of an AP is \(24\) and the 8th term is \(33\). The common difference is:
13
The 5th term of an AP with \(a = 4\) and \(d = 7\) is:
14
The sequence \(2, 5, 8, 11, \ldots\) has:
15
If the 10th term of an AP is \(25\) and the 15th term is \(45\), then the common difference is:
16
For an AP with first term \(a = 2\) and \(d = 2\), the value of \(S_{10} - S_5\) is:
17
The first term of an AP is \(7\) and the 7th term is \(28\). The common difference is:
18
Which term of the AP \(3, 7, 11, 15, \ldots\) is \(83\)?
19
The sum of the first 15 natural numbers using AP formula is:
20
If the first term of an AP is \(5\) and the common difference is \(3\), then the 12th term is:
21
In an AP, if \(a_3 = 9\) and \(a_7 = 25\), then \(a\) is:
22
The number of terms in the AP \(20, 18, 16, \ldots, 2\) is:
23
Which term of the AP \(7, 12, 17, 22, \ldots\) is \(92\)?
24
The 8th term of the AP whose first term is \(2\) and common difference is \(3\) is:
25
The sum of the first 10 terms of the AP \(2, 5, 8, 11, \ldots\) is:
26
The 10th term of an AP is \(46\) and the common difference is \(5\). The first term is:
27
The sum of the first 20 terms of the AP \(5, 8, 11, 14, \ldots\) is:
28
The arithmetic mean of \(12\) and \(24\) is:
29
If the sum of first \(n\) terms of an AP is \(S_n = 5n^2 + 3n\), then the first term is:
30
For the same AP in Q29, the common difference is:
31
The 15th term of the AP \(8, 13, 18, 23, \ldots\) is:
32
The number of terms in the AP \(7, 13, 19, \ldots, 97\) is:
33
The sum of first 7 terms of the AP \(3, 6, 9, \ldots\) is:
34
The sum of the first 50 terms of the AP \(2, 4, 6, \ldots\) is:
35
An AP has first term \(5\) and common difference \(3\). The sum of its first 12 terms is:
36
How many terms of the AP \(4, 7, 10, 13, \ldots\) are needed to make a sum of \(144\)?
37
The 15th term from the end of the AP \(6, 9, 12, \ldots, 96\) is:
38
If the sum of first 6 terms of an AP is \(54\) and the first term is \(3\), then the common difference is:
39
In an AP, the sum of first 5 terms is \(35\) and the first term is \(3\). The common difference is:
40
In an AP, the 4th term is \(10\) and the 10th term is \(22\). The common difference is:
41
For the AP of Q40, the first term \(a\) is:
42
Which of the following is NOT a property of an AP?
43
The 9th term of the AP \(2, 5, 8, 11, \ldots\) is:
44
The sum of the first 8 terms of AP \(7, 10, 13, 16, \ldots\) is:
45
In an AP, the first term is \(4\) and the 6th term is \(19\). The common difference is:
46
In an AP, if \(a = 2\) and \(d = 5\), then the sum of first 5 terms is:
47
The 3rd, 8th and 13th terms of an AP are:
48
In an AP, if the 7th term is \(20\) and the 13th term is \(38\), then the common difference is:
49
In an AP, if the 4th term is \(11\) and the common difference is \(2\), then the first term is:
50
In an AP, if the sum of the first \(n\) terms is \(S_n = 2n^2 + 3n\), then the 10th term is:
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Frequently Asked Questions

A sequence of numbers where the difference between consecutive terms is constant.

The fixed amount added or subtracted to obtain the next term.

Subtract any term from the next: \(d = a_2 - a_1\).

\(a_n = a + (n - 1)d\).

The initial term, denoted by \(a\).

To find any term without listing all previous terms.

\(l = a + (n - 1)d\)

An AP with a fixed number of terms.

An AP that continues indefinitely.

\(S_n = \dfrac{n}{2}\Bigl [2a + (n - 1)d\Bigr]\)

\(S_n = \frac{n}{2} (a + l)\)

Verify if consecutive differences are equal.

Solve \(a + (n - 1)d =\) term and check if n is a positive integer.

The AP grows as n increases.

The AP decreases as n increases.

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