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CBSE Class 10  >  Class 10 Test  >  Olympiad Preparation  >  Math Olympiad Test: Arithmetic Progression- 3 - Class 10 MCQ

Math Olympiad Test: Arithmetic Progression- 3 - Class 10 Free MCQ


MCQ Practice Test & Solutions: Math Olympiad Test: Arithmetic Progression- 3 (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- 3". 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- 3 - Question 1
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Find the sum of first 20 terms of an A.P. whose nth term is given by Tn = (7 – 3n).

Detailed Solution: Question 1

We have, Tn = (7 – 3n)
First term, T1 = (7 – 3 × 1) = 4
Second term, T2 = 7 – 3 × 2 = 1
Third term, T3 = 7 – 3 × 3 = –2
∴ Series is 4, 1, – 2, .......... and common difference = –3
Sum of first 20 terms (S20)
= 20/2 [24 (20 - 1)(- 3)] = 10 [8 – 57] = –490

Math Olympiad Test: Arithmetic Progression- 3 - Question 2
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If 9th term of an A.P. is zero, then its 29th term is ________ its 19th term.

Detailed Solution: Question 2

Let 1st term of A.P. be a and common difference be d.
Now, a9 = 0 ⇒ a + 8d = 0 ⇒ a = –8d ...(i)
Now, a29 = a + 28d = –8d + 28d
⇒ a29 = 20d ...(ii)
Also, a19 = a + 18d = –8d + 18d = 10d
⇒ 2 × a19 = 2 × 10d = 20d ...(iii)
From (ii) and (iii), we have
a29 = 2a19

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Math Olympiad Test: Arithmetic Progression- 3 - Question 3
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Which term of the A.P. 5, 2, –1, ....... is –22? 

Detailed Solution: Question 3

Given A.P. is 5, 2, –1, ......
⇒ a = 5, d = 2 – 5 = –3
Tn = – 22 ⇒ a + (n – 1)d = –22
⇒ 5 + (n – 1) (–3) = –22 ⇒ n = 10
Hence, 10th term of the given A.P. is –22.

Math Olympiad Test: Arithmetic Progression- 3 - Question 4
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In an A. P., the sum of first n terms is  Find its 25th term.

Detailed Solution: Question 4

We have given that 
25th term = Sum of 25 terms – Sum of 24 terms
= S25 – S24
Now, S25 = 1100 and S24 = 1020
∴ 25th term = 1100 – 1020 = 80

Math Olympiad Test: Arithmetic Progression- 3 - Question 5
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In an A.P., if the pth term is ‘q’ and the qth term is ‘p’, then its nth term is ________.

Detailed Solution: Question 5

We have given that ap = q and aq = p
⇒ q = a + (p – 1)d and ... (i)
p = a + (q – 1)d ... (ii)
Subtracting (ii) from (i), we get
q – p = d (p – q) ⇒ d = –1
Now, q = a + 1 – p [From (i)]
⇒ a = q + p – 1
∴ an = a + (n – 1) d = q + p – 1 + (n – 1) (– 1)
= q + p – 1 + 1 – n = q + p – n

Math Olympiad Test: Arithmetic Progression- 3 - Question 6
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The sum of all terms of the arithmetic progression having ten terms except for the first term, is 99, and except for the sixth term, is 89. Find the 8th term of the progression if the sum of the first and the fifth term is equal to 10.

Detailed Solution: Question 6

According to the question, we have
a2 + ....... + a10 = 99 ... (i)
and a1 + ....... + a5 + a7 +..... + a10 = 89 ... (ii)
Subtracting (ii) from (i), we get
⇒ a6 – a1 = 10 ⇒ a1 + 5d – a1 = 10
⇒ 5d = 10 ⇒ d = 2
Also, a1 + a5 = 10 ⇒ a1 + a1 + 4d = 10
⇒ 2a1 + 8 = 10 ⇒ a1 = 1
∴ 8th term = a1 + 7d = 1 + 14 = 15

Math Olympiad Test: Arithmetic Progression- 3 - Question 7
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The ratio of the sum of m and n terms of an A.P. is m2 : n2, then find the ratio of mth and nth terms.

Detailed Solution: Question 7

We have, given that, 

Replacing m with 2m – 1 and n with 2n – 1, we get

Math Olympiad Test: Arithmetic Progression- 3 - Question 8
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If x ≠ y and the sequences x, a1, a2, y and x, b1, b2, y each are in A.P., then  is ________.

Detailed Solution: Question 8

For sequence, x, a1, a2, y
y = x + 3d ⇒ d = (y - x)/3

Similarly, 
For sequence, x, b1, b2, y

Math Olympiad Test: Arithmetic Progression- 3 - Question 9
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If the mth term of an A.P. is 1/n and nth term is 1/m, then the sum of first mn terms is _______.

Detailed Solution: Question 9

We have given, 
Then, a + (m-1)d = 1/n ...(i)
And, a + (n-1)d = 1/m ... (ii)
Subtracting (ii) from (i), we get,

 [From (i)]

Now, 

Math Olympiad Test: Arithmetic Progression- 3 - Question 10
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Four numbers are inserted between the numbers 4 and 39 such that an A.P. results. Find the biggest of these four numbers.

Detailed Solution: Question 10

Since 4 terms are inserted between 4 and 39 so there are 6 terms in the AP
Therefore, the terms of the AP ar given by: 4, 4 + d, 4 + 2d, 4 + 3d, 4 + 4d, 4+5d
⇒ 39 = 4 + 5d,
⇒ d = 7,
So, as it is an increasing AP, therefore 4+4d would be the biggest.
⇒ 4 + 4d = 4 + 4 × 7 = 4 + 28 = 32.

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About this Class 10 Practice Test

This test contains 10 MCQs on Math Olympiad Test: Arithmetic Progression- 3 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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