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CBSE Class 10  >  Class 10 Test  >  Olympiad Preparation  >  Math Olympiad Test: Arithmetic Progression- 1 - Class 10 MCQ

Math Olympiad Test: Arithmetic Progression- 1 - Class 10 Free MCQ


MCQ Practice Test & Solutions: Math Olympiad Test: Arithmetic Progression- 1 (10 Questions)

You can prepare effectively for Class 10 Olympiad Preparation for Class 10 with this dedicated MCQ Practice Test (available with solutions) on the important topic of "Math Olympiad Test: Arithmetic Progression- 1". These 10 questions have been designed by the experts with the latest curriculum of Class 10 2026, to help you master the concept.

Test Highlights:

  • - Format: Multiple Choice Questions (MCQ)
  • - Duration: 10 minutes
  • - Number of Questions: 10

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Math Olympiad Test: Arithmetic Progression- 1 - Question 1
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If S1, S2, S3, …. Sm are the sum of n terms of m arithmetic progression whose first terms are 1, 2, 3, …. m and common differences are 1, 3, 5, … (2m - 1) respectively. What is the value of S1 + S2 + …. Sm?

Detailed Solution: Question 1



Math Olympiad Test: Arithmetic Progression- 1 - Question 2
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If the 3rd and 7th terms of an arithmetic progression are 17 and 27 respectively. Find the first term of arithmetic progression.

Detailed Solution: Question 2

Let a be the first term and d be the common difference
a + 2d = 17
a + 6d = 27
Solving these eqns we get a = 12

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Math Olympiad Test: Arithmetic Progression- 1 - Question 3
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If four numbers in arithmetic progression are such that their sum is 50 and the greatest number is 4 times the least. Which number is the least one?

Detailed Solution: Question 3

Let the numbers are a -3d, a - d, a + d, a + 3d
a - 3d + a - d + a + d + a + 3d = 50
⇒ 4a = 50 ⇒ a = 50/4 = 25/2
a + 3d = 4(a - 3d )
⇒ a + 3d = 4a - 12d
⇒ 3a = 15d
⇒ a = 5d
⇒ 25/2 = 5d
⇒ d = 5/2

Math Olympiad Test: Arithmetic Progression- 1 - Question 4
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If 8th term of an arithmetic progression is 31 and its 15th term is 16 more than 11th term of the arithmetic progression. What is the first term of that arithmetic progression?

Detailed Solution: Question 4

Let a be the first term and d be the common difference
a + 7d = 31
a + 14d = a + 10d + 16
a + 14d - a - 10d = 16
⇒ d = 4
∴ a = 31 - 7d = 31 - 28 = 3

Math Olympiad Test: Arithmetic Progression- 1 - Question 5
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What is the sum of first 30 terms of the arithmetic progression whose 2nd term is 8 and 4th term is 14?

Detailed Solution: Question 5

Let a be the first term and d be common difference
∴ a + d = 8; a + 3d = 14

= 15 [10 + 87] = 15 × 97 = 1455

Math Olympiad Test: Arithmetic Progression- 1 - Question 6
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Find the sum of first 25 terms of an arithmetic progression whose nth term is given by 7 - 3n.

Detailed Solution: Question 6

tn = 7 - 3n
t1 = 7 - 3 × 1 = 4 ⇒ a = 4
t2 = 7 - 3 × 2 = 1
d = 1 - 4 = -3

Math Olympiad Test: Arithmetic Progression- 1 - Question 7
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The first term of an arithmetic progression is 2 and the last term is 50. The sum of all these terms is 442. What is the common difference?

Detailed Solution: Question 7

a = 2 , l = 50


Math Olympiad Test: Arithmetic Progression- 1 - Question 8
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The sum of the three numbers in arithmetic progression is 12. The sum of their cubes is 288. What are the numbers?

Detailed Solution: Question 8

Let the numbers be a - d, a, a + d.
a - d + a + a + d = 12 ⇒ 3a = 12 ⇒ a = 4
and (a - d)3 + a3 + (a + d)3 = 288
a3 - d3 - 3ad(a - d) + a3 + a3 + d3 + 3ad(a + d) = 288
a3 - d3 - 3ad(a - d) + a3 + a3 + a3 + 3ad + 3ad2 = 288
⇒ 3a3 + 6ad2 = 288 ⇒ 3 × 43 + 6 × 4 × d2 = 288
⇒ 24d2 = 288 - 192
⇒ d2 = 95/24 = 4
⇒ d = ±2

Math Olympiad Test: Arithmetic Progression- 1 - Question 9
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If the sum of n terms of an Arithmetic Progression is given by Sn = 3n2 + 2n. Find its first term and common difference.

Detailed Solution: Question 9

Given Sn = 3n2 + 2n
∴ S1 = 3 × 12 + 2 × 1 = 5
S2 = 3 × 22 + 2 × 2 = 16
The sequence is 5, 11, …..
a = 5 , d = 11 - 5 = 6

Math Olympiad Test: Arithmetic Progression- 1 - Question 10
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How many terms are there in the Arithmetic Progression?
7, 11, 15, …..139?

Detailed Solution: Question 10

Given AP is 7, 11, 15, ….139
Here a = 7, d = 11 - 7 = 4, l = 139
l = a + (n - 1) d
⇒ 139 = 7 + (n - 1) 4

⇒ n = 34

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About this Class 10 Practice Test

This test contains 10 MCQs on Math Olympiad Test: Arithmetic Progression- 1 with detailed solutions for each question. It is part of the Olympiad Preparation for Class 10 course on EduRev, designed to align with the current Class 10 syllabus. Each solution explains not just the correct answer but also gives you an understanding of the topic — not just to attempt the question but also help you prepare for the exam with practice.

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