CBSE BOARD PYQS · CHAPTER 05

Arithmetic Progressions
CBSE Most Repeated PYQs

Solve official CBSE Previous Year Board Questions (2015-2024) for Arithmetic Progressions. Click on options to test yourself, or click "Show Solution & Answer" for complete step-by-step working.

Q1CBSE 2024, 2020MCQ

1 Mark

The 10th term of the AP: 2, 7, 12, ... is:

Q2CBSE 2023, 2019MCQ

1 Mark

Which term of the AP: 21, 18, 15, ... is 0?

Q3CBSE 2022, 2018MCQ

1 Mark

The sum of first 20 positive integers is:

Q4CBSE 2024, 2021MCQ

1 Mark

If the nth term of an AP is (3n + 7), then its common difference is:

Q5CBSE 2023, 2017Assertion-Reason

1 Mark

Assertion (A): The sum of first n terms of an AP is given by Sₙ = n/2 [2a + (n-1)d]. Reason (R): The nth term aₙ of an AP can be found using formula aₙ = Sₙ - Sₙ₋₁.

Q6CBSE 2020, 2016Assertion-Reason

1 Mark

Assertion (A): The sequence 4, 10, 16, 22, ... forms an AP with common difference 6. Reason (R): A sequence a₁, a₂, a₃ ... forms an AP if difference (aₖ₊₁ - aₖ) is constant.

Q7CBSE 2024, 2020Short Answer

2 Marks

Find the 11th term from the end of the AP: 10, 7, 4, ..., -62.

Q8CBSE 2023, 2019Short Answer

2 Marks

How many two-digit numbers are divisible by 3?

Q9CBSE 2022, 2018Short Answer

2 Marks

Find the sum of first 15 multiples of 8.

Q10CBSE 2024, 2021Short Answer

2 Marks

If 17th term of an AP exceeds its 10th term by 7, find the common difference.

Q11CBSE 2023, 2017Short Answer

2 Marks

Find the sum: 7 + 10½ + 14 + ... + 84.

Q12CBSE 2020, 2016Long Answer

3 Marks

The 4th and 8th terms of an AP are 24 and 44 respectively. Find the first three terms.

Q13CBSE 2024, 2020Long Answer

3 Marks

How many terms of AP: 24, 21, 18, ... must be taken so that their sum is 78?

Q14CBSE 2023, 2019Long Answer

3 Marks

If the sum of first n terms of an AP is 4n - n², find the 1st term, 2nd term and 10th term.

Q15CBSE 2022, 2018Long Answer

3 Marks

A sum of ₹700 is used to give 7 cash prizes. Each prize is ₹20 less than preceding. Find value of each prize.

Q16CBSE 2024, 2021Case Study

4 Marks

Case Study Scenario: A manufacturer of TV sets produced 600 sets in 3rd year and 700 sets in 7th year. Assuming uniform annual increase. Question: Find total production in first 7 years.

Q17CBSE 2023, 2017Case Study

4 Marks

Case Study Scenario: 200 logs are stacked: 20 in bottom row, 19 in next, 18 in next and so on. Question: Find how many rows are logs placed in and logs in top row.

Q18CBSE Official Board PYQPYQ

5 Marks

If m times mth term of an AP is equal to n times nth term, show that (m+n)th term is 0.

Q19CBSE Official Board PYQPYQ

5 Marks

The ratio of 11th term to 18th term of an AP is 2 : 3. Find ratio of 5th term to 21st term.

Q20CBSE Official Board PYQPYQ

5 Marks

Arithmetic Progressions CBSE Most Repeated PYQs

The 10th term of the AP: 2, 7, 12, ... is:

Which term of the AP: 21, 18, 15, ... is 0?

The sum of first 20 positive integers is:

If the nth term of an AP is (3n + 7), then its common difference is:

Assertion (A): The sum of first n terms of an AP is given by Sₙ = n/2 [2a + (n-1)d]. Reason (R): The nth term aₙ of an AP can be found using formula aₙ = Sₙ - Sₙ₋₁.

Assertion (A): The sequence 4, 10, 16, 22, ... forms an AP with common difference 6. Reason (R): A sequence a₁, a₂, a₃ ... forms an AP if difference (aₖ₊₁ - aₖ) is constant.

Find the 11th term from the end of the AP: 10, 7, 4, ..., -62.

How many two-digit numbers are divisible by 3?

Find the sum of first 15 multiples of 8.

If 17th term of an AP exceeds its 10th term by 7, find the common difference.

Find the sum: 7 + 10½ + 14 + ... + 84.

The 4th and 8th terms of an AP are 24 and 44 respectively. Find the first three terms.

How many terms of AP: 24, 21, 18, ... must be taken so that their sum is 78?

If the sum of first n terms of an AP is 4n - n², find the 1st term, 2nd term and 10th term.

A sum of ₹700 is used to give 7 cash prizes. Each prize is ₹20 less than preceding. Find value of each prize.

Case Study Scenario: A manufacturer of TV sets produced 600 sets in 3rd year and 700 sets in 7th year. Assuming uniform annual increase. Question: Find total production in first 7 years.

Case Study Scenario: 200 logs are stacked: 20 in bottom row, 19 in next, 18 in next and so on. Question: Find how many rows are logs placed in and logs in top row.

If m times mth term of an AP is equal to n times nth term, show that (m+n)th term is 0.

The ratio of 11th term to 18th term of an AP is 2 : 3. Find ratio of 5th term to 21st term.

Find sum of all 3-digit natural numbers which leave remainder 2 when divided by 7.

Arithmetic Progressions
CBSE Most Repeated PYQs