aₙ = a+(n−1)d Sₙ = n/2·[2a+(n−1)d] a₁ a₂ a₃ a₄ a₅ a₆ → +d
a,a+d,…
Chapter 5  ·  Class X Mathematics  ·  MCQ Practice

MCQ Practice Arena

Arithmetic Progressions

Two Formulae, Full Marks — Make AP Your Fastest Chapter

📋 50 MCQs ⭐ 32 PYQs ⏱ 55 sec/Q
🚀 Start Practising 📖 Revise Notes First

MCQ Bank Snapshot

50Total MCQs
24Easy
18Medium
8Hard
32PYQs
55 secAvg Time/Q
6Topics
Easy 48% Medium 36% Hard 16%

Why Practise These MCQs?

CBSE Class XNTSEState BoardsOlympiad

Arithmetic Progressions is the most formula-direct chapter in Class X — almost every MCQ reduces to applying aₙ = a+(n−1)d or Sₙ = n/2[2a+(n−1)d]. CBSE Boards assign 8–10 marks here; the pattern is predictable and achievable in 2 days. NTSE uses elegant AP problems with algebraic conditions. Target 100% accuracy in this chapter.

Topic-wise MCQ Breakdown

Identify Whether Sequence is AP6 Q
Common Difference d5 Q
nth Term aₙ14 Q
Sum of n Terms Sₙ14 Q
Arithmetic Mean4 Q
Mixed — Both aₙ and Sₙ Required7 Q

Must-Know Formulae Before You Start

Recall these cold before attempting MCQs — they appear in >70% of questions.

$a_n = a + (n-1)d$
$S_n = \tfrac{n}{2}[2a + (n-1)d]$
$S_n = \tfrac{n}{2}[a + l]\ (l = \text{last term})$
$\text{AM of } a \text{ and } b = (a+b)/2$
$d = a_2 - a_1\ (\text{constant throughout})$

MCQ Solving Strategy

Every AP MCQ has just two formulae — learn which one to use. If the question gives or asks about a specific TERM, use aₙ. If it gives or asks about a SUM, use Sₙ. When both are needed, set up two equations from two conditions and solve simultaneously. "Middle term of AP" = Sₙ/n = arithmetic mean. For "sum of first n odd/even numbers" — these follow AP directly.

⚠ Common Traps & Errors

Difficulty Ladder

Work through each rung in order — do not jump to Hard before mastering Easy.

① Easy

Check if sequence is AP, find d, compute aₙ for small n

② Medium

Find Sₙ, find n given Sₙ, arithmetic mean problems

③ Hard

Two-condition AP systems, sum of specific term ranges

★ PYQ

CBSE — find nth term + sum combo; NTSE — algebraic AP conditions

Continue Your Preparation

📖 Chapter Notes Revise concepts & theory 🧠 MCQ Practice Topic-wise Questions 📘✔️ Exercises Step-by-step NCERT solutions ✔️❌ True / False Concept-based True & False ➡ Next Chapter Triangles
🎯 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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Arithmetic Progressions | Maths Class 10
Arithmetic Progressions | Maths Class 10 — Complete Notes & Solutions · academia-aeternum.com
🎓 Class 10 📐 Maths 📖 NCERT ✅ Free Access 🏆 CBSE · JEE
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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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    ACADEMIA AETERNUM तमसो मा ज्योतिर्गमय · Est. 2025
    Sharing this chapter
    Arithmetic Progressions | Mathematics Class -10
    Arithmetic Progressions | Mathematics Class -10 — Complete Notes & Solutions · academia-aeternum.com
    🎓 Class -10 📐 Mathematics 📖 NCERT ✅ Free Access 🏆 CBSE · JEE
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    academia-aeternum.com/class-10/mathematics/arithmetic-progressions/mcqs/ Copy link
    💡
    Exam tip: Sharing chapter notes with your study group creates a reinforcement loop. Teaching a concept is the fastest path to mastering it.

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