Arithmetic Progressions helps students understand how numbers follow a consistent pattern and how mathematical formulas can be used to solve sequence-based problems. The chapter covers common differences, terms of an arithmetic progression, and the sum of terms, helping students improve logical reasoning and calculation skills. Practicing Arithmetic Progressions MCQs regularly strengthens formula application and prepares students for objective questions in Class 10 Maths.
Understanding number patterns and their relationships makes it easier to solve problems accurately and confidently. Students can practice chapter-wise MCQs and explore Class 10 MCQs for focused revision. Additional CBSE Board resources can help students prepare for objective questions based on the latest syllabus and exam pattern.
Main Concepts of Arithmetic Progressions
Before solving Arithmetic Progressions MCQs with Answers, students should revise all important concepts carefully because many objective questions are directly formula and pattern based. Important topics covered in this chapter :
- Arithmetic progression basics
- Meaning of sequence
- First term of AP
- Common difference
- nth term formula
- Sum of n terms
- Increasing arithmetic progression
- Decreasing arithmetic progression
- Finite sequence
- Consecutive terms
- Pattern observation
- Formula-based calculations
- Sequence simplification
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MCQs for Class 10 Maths Chapter 5 with Answers and Explanations
Build confidence in Arithmetic Progression by solving these Class 10 Maths MCQs and revising important concepts. These objective questions help students improve formula application, sequence analysis, numerical reasoning, and calculation accuracy for school exams and board preparation.
Q1. In an Arithmetic Progression, the common difference is -4 and the 7th term is 4. Find the first term.
A) 24
B) 20
C) 28
D) 32
Answer: C
Explanation: Using the formula:
an = a + (n - 1)d
4 = a + (7 - 1)(-4)
4 = a - 24
a = 28
Q2. If the first term of an AP is 3.5 and the common difference is 0, then the 101st term is:
A) 0
B) 3.5
C) 103.5
D) 101
Answer: B
Explanation: When d = 0, all terms remain equal.
a101 = 3.5 + (101 - 1)(0)
a101 = 3.5
Q3. The sequence -10, -6, -2, 2, ... is:
A) An AP with d = -4
B) Not an AP
C) An AP with d = 4
D) A geometric progression
Answer: C
Explanation:
-6 - (-10) = 4
-2 - (-6) = 4
2 - (-2) = 4
Since the difference is constant, it is an AP.
Q4. Find the 11th term of the AP: -5, -5/2, 0, 5/2, ...
A) -20
B) 20
C) 30
D) -30
Answer: B
Explanation:
a = -5
d = -5/2 - (-5)
d = -5/2 + 10/2
d = 5/2
a11 = a + 10d
a11 = -5 + 10(5/2)
a11 = -5 + 25
a11 = 20
Q5. Which set correctly represents the first four terms of an AP having first term -2 and common difference -2?
A) -2, 0, 2, 4
B) -2, -4, -6, -8
C) -2, -6, -10, -14
D) -2, -4, -8, -16
Answer: B
Explanation:
a1 = -2
a2 = -2 + (-2) = -4
a3 = -4 + (-2) = -6
a4 = -6 + (-2) = -8
Q6. The first two terms of an AP are -3 and 4. Find the 21st term.
A) 137
B) 143
C) 17
D) -143
Answer: A
Explanation:
a = -3
d = 4 - (-3)
d = 7
a21 = a + 20d
a21 = -3 + 20(7)
a21 = -3 + 140
a21 = 137
Q7. In an AP, the 2nd term is 13 and the 5th term is 25. Find the 7th term.
A) 30
B) 33
C) 37
D) 38
Answer: B
Explanation:
a + d = 13
a + 4d = 25
Subtracting:
3d = 12
d = 4
a + 4 = 13
a = 9
a7 = a + 6d
a7 = 9 + 24
a7 = 33
Q8. Which term of the AP 21, 42, 63, 84, ... is 210?
A) 9th
B) 10th
C) 11th
D) 12th
Answer: B
Explanation:
a = 21
d = 21
an = a + (n - 1)d
210 = 21 + (n - 1)(21)
210 = 21n
n = 10
Q9. If the common difference of an AP is 5, then find: a18 - a13
A) 5
B) 20
C) 25
D) 30
Answer: C
Explanation:
a18 = a + 17d
a13 = a + 12d
a18 - a13 = 5d
= 5 × 5
= 25
Q10. The nth term of an AP is given by: an = 3 + 4n. Find the common difference.
A) 7
B) 3
C) 4
D) 1
Answer: C
Explanation:
a1 = 3 + 4(1)
a1 = 7
a2 = 3 + 4(2)
a2 = 11
d = 11 - 7
d = 4
Q11. If the first three terms of an AP are: 3y - 1, 3y + 5, 5y + 1
then find y.
A) 2
B) 3
C) 4
D) 5
Answer: D
Explanation:
(3y + 5) - (3y - 1) = (5y + 1) - (3y + 5)
6 = 2y - 4
2y = 10
y = 5
Q12. Find the common difference of: 1/2q, (1 - 2q)/2q, (1 - 4q)/2q, ...
A) -1
B) 1
C) q
D) -q
Answer: A
Explanation:
d = (1 - 2q)/2q - 1/2q
d = (1 - 2q - 1)/2q
d = -2q/2q
d = -1
Q13. If 18, a, b, -3 are in AP, then find a and b.
A) 11, 4
B) 12, 6
C) 13, 8
D) 14, 7
Answer: A
Explanation:
-3 = 18 + 3d
3d = -21
d = -7
a = 18 - 7
a = 11
b = 11 - 7
b = 4
Q14. Find the 4th term from the end of the AP: -11, -8, -5, ..., 49
A) 37
B) 40
C) 43
D) 46
Answer: B
Explanation:
Last term = 49
d = 3
Required term = 49 - (4 - 1)(3)
= 49 - 9
= 40
Q15. If the first term of an AP is 3 and common difference is 4, find the 10th term.
A) 39
B) 43
C) 47
D) 53
Answer: A
Explanation:
a10 = 3 + (10 - 1)(4)
= 3 + 36
= 39
Q16. The sum of the first 15 terms of an AP is 255. If the first term is 3, find the common difference.
A) 1
B) 2
C) 3
D) 4
Answer: B
Explanation:
Using:
Sn = n/2 [2a + (n - 1)d]
255 = 15/2 [2(3) + 14d]
255 = 15/2 [6 + 14d]
34 = 6 + 14d
14d = 28
d = 2
Q17. The sum of the first n terms of an AP is: Sn = 6n² - 2n. Find n when Sn = 1320.
A) 12
B) 13
C) 14
D) 15
Answer: D
Explanation:
6n² - 2n = 1320
3n² - n - 660 = 0
3n² - 45n + 44n - 660 = 0
3n(n - 15) + 44(n - 15) = 0
(n - 15)(3n + 44) = 0
n = 15
Q18. Determine the first term and common difference of the AP: 3, 1, -1, -3, ...
A) 1, 3
B) -1, 3
C) 3, -2
D) 2, 3
Answer: C
Explanation:
First term:
a = 3
Common difference:
d = 1 - 3
d = -2
Q19. If the (p + q)th term of an AP is m and the (p - q)th term is n, then the pth term equals:
A) m + n
B) (m - n)/2
C) (m + n)/2
D) mn
Answer: C
Explanation:
ap+q = a + (p + q - 1)d = m
ap-q = a + (p - q - 1)d = n
Adding both:
2a + (2p - 2)d = m + n
2[a + (p - 1)d] = m + n
ap = (m + n)/2
Q20. Find the sum of all two-digit odd numbers.
A) 2425
B) 2475
C) 2525
D) 2575
Answer: B
Explanation:
AP:
11, 13, 15, ..., 99
a = 11
l = 99
d = 2
99 = 11 + (n - 1)2
88 = 2(n - 1)
n = 45
Sum:
S = n/2 (a + l)
S = 45/2 (11 + 99)
S = 45/2 × 110
S = 2475
Q21. The sum of the first n odd natural numbers is:
A) 2n²
B) 2n + 1
C) 2n - 1
D) n²
Answer: D
Explanation:
1 + 3 + 5 + ... + (2n - 1)
Sn = n/2 [2 + (n - 1)2]
= n/2 (2n)
= n²
Q22. If a, b, and c are in AP, then which relation is correct?
A) a + c = 2b
B) a + b = 2c
C) c = (a + b)/2
D) a + c = b
Answer: A
Explanation:
For AP:
b - a = c - b
2b = a + c
a + c = 2b
Q23. The sum of the 6th and 7th terms of an AP is 39. If d = 3, find the first term.
A) 2
B) -3
C) 4
D) 3
Answer: D
Explanation:
a6 = a + 5d
a7 = a + 6d
(a + 5d) + (a + 6d) = 39
2a + 11d = 39
2a + 33 = 39
2a = 6
a = 3
Q24. Three numbers are in AP and their sum is 30. If the greatest number is 13, find the common difference.
A) 2
B) 4
C) 5
D) 3
Answer: D
Explanation:
Let numbers be:
a - d, a, a + d
Sum:
3a = 30
a = 10
Largest number:
10 + d = 13
d = 3
Q25. Find the common difference of the AP: 1/8, 2/8, 3/8, ...
A) 1/8
B) 1
C) 1/4
D) 1/2
Answer: A
Explanation:
d = 2/8 - 1/8
d = 1/8
Q26. How many natural numbers less than or equal to 300 are divisible by 17?
A) 13
B) 15
C) 17
D) 19
Answer: C
Explanation:
Multiples of 17:
17, 34, 51, ..., 289
289 = 17 × 17
Hence, total numbers = 17
Q27. Find the first negative term of the AP: 81/5, 77/5, 73/5, ...
A) 20th
B) 21st
C) 22nd
D) 23rd
Answer: C
Explanation:
a = 81/5
d = -4/5
an = a + (n - 1)d
81/5 + (n - 1)(-4/5) < 0
81 - 4n + 4 < 0
85 < 4n
n > 21.25
First integer value:
n = 22
Q28. If: Sn = n(n - 1) then the nth term of the AP is:
A) 2n
B) 2n - 1
C) 2n - 2
D) 2n - 4
Answer: C
Explanation:
an = Sn - Sn-1
an = n(n - 1) - (n - 1)(n - 2)
an = (n² - n) - (n² - 3n + 2)
an = 2n - 2
Q29. The first term of an AP is -12 and the 6th term is 8. If the sum of first n terms is 120, find n.
A) 10
B) 11
C) 12
D) 13
Answer: C
Explanation:
a = -12
a6 = a + 5d
8 = -12 + 5d
5d = 20
d = 4
Now:
120 = n/2 [2(-12) + (n - 1)4]
240 = n(-24 + 4n - 4)
240 = n(4n - 28)
4n² - 28n - 240 = 0
n² - 7n - 60 = 0
(n - 12)(n + 5) = 0
n = 12
Q30. If 2x, x + 10, and 3x + 2 are consecutive terms of an AP, then x equals:
A) 4
B) 5
C) 6
D) 8
Answer: C
Explanation: For consecutive terms in AP:
2(x + 10) = 2x + (3x + 2)
2x + 20 = 5x + 2
18 = 3x
x = 6
Important Formulas Used in Arithmetic Progressions
nth Term Formula
an = a + (n − 1)d
This formula is used to calculate any specific term of the arithmetic progression directly.
Sum of n Terms Formula
Sn = n/2 [2a + (n − 1)d]
This formula helps calculate the sum of multiple terms quickly without adding every term individually.
Meaning of Formula Variables
a = first term
d = common difference
n = number of terms
an = nth term
Sn = sum of n terms
Mistakes Students Make in Arithmetic Progressions MCQs
Many students lose marks in Arithmetic Progressions MCQs because of small calculation or observation errors. Common mistakes :
- Wrong common difference calculation
- Incorrect term counting
- Formula substitution mistakes
- Sign errors in decreasing AP
- Confusion between nth term and sum formulas
- Arithmetic simplification errors
- Skipping calculation steps
