Kerala SSLC Maths Chapter 1: Arithmetic Sequences Important Questions

Arithmetic Sequences is an important chapter in Kerala SSLC Class 10 Mathematics. Practising Important Questions for Kerala SSLC Maths Chapter 1 helps students understand different question types, such as identifying sequence patterns, forming algebraic expressions, and solving word problems. Understanding these concepts helps students solve problems accurately and prepare for board examinations.

Students should practise finding the nth term, calculating the sum of terms, and identifying the common difference. Solving different types of questions with proper steps helps strengthen mathematical concepts and improve exam preparation.

Kerala Class 10 Chapter 1 Arithmetic Sequences Important Questions 

Practising essential questions from Kerala SSLC Maths helps students understand important concepts and exam patterns. Students can also refer to the Kerala SSLC Maths Model Paper for additional practice and a better understanding of the question format. Below are key Arithmetic Sequences questions with step-by-step solutions.

Q1. Find the number of dots in each triangle and calculate the number of dots needed to make the next three triangles in the pattern.

Solution:

The number of dots in the given triangles forms the sequence:

3, 6, 10, ...

The differences between consecutive terms are:

6 − 3 = 3

10 − 6 = 4

The next differences will be 5, 6, and 7.

Therefore:

• Fourth triangle = 10 + 5 = 15 dots

• Fifth triangle = 15 + 6 = 21 dots

• Sixth triangle = 21 + 7 = 28 dots

Answer: 15, 21, and 28 dots.

Q2. Find the sequence of sums of interior angles of regular polygons having 3, 4, 5, 6, ... sides.

Solution:

The sum of interior angles of a polygon is calculated using:

Sum of interior angles = (n − 2) × 180°

Here, n represents the number of sides.

• Triangle (3 sides) = (3 − 2) × 180° = 180°

• Square (4 sides) = (4 − 2) × 180° = 360°

• Pentagon (5 sides) = (5 − 2) × 180° = 540°

• Hexagon (6 sides) = (6 − 2) × 180° = 720°

Answer: 180°, 360°, 540°, 720°, ...

Q3. Find the sequence of sums of exterior angles of regular polygons having 3, 4, 5, 6, ... sides.

Solution:

The sum of exterior angles of any polygon is always 360°.

Therefore:

• Triangle = 360°

• Square = 360°

• Pentagon = 360°

• Hexagon = 360°

Answer: 360°, 360°, 360°, 360°, ...

Q4. Write the sequence of measures of one interior angle of regular polygons having 3, 4, 5, 6, ... sides.

Solution:

The measure of one interior angle of a regular polygon is:

One interior angle = [(n − 2) × 180°] ÷ n

Calculating for each polygon:

• Triangle = [(3 − 2) × 180°] ÷ 3 = 60°

• Square = [(4 − 2) × 180°] ÷ 4 = 90°

• Pentagon = [(5 − 2) × 180°] ÷ 5 = 108°

• Hexagon = [(6 − 2) × 180°] ÷ 6 = 120°

Answer: 60°, 90°, 108°, 120°, ...

Q5. Write the sequence of measures of one exterior angle of regular polygons having 3, 4, 5, 6, ... sides.

Solution:

The measure of one exterior angle of a regular polygon is:

One exterior angle = 360° ÷ n

Therefore:

• Triangle = 360° ÷ 3 = 120°

• Square = 360° ÷ 4 = 90°

• Pentagon = 360° ÷ 5 = 72°

• Hexagon = 360° ÷ 6 = 60°

Answer: 120°, 90°, 72°, 60°, ...

Q6. Write the sequence of natural numbers that leave a remainder of 1 when divided by 3.

Solution:

The natural numbers that leave a remainder of 1 when divided by 3 are:

• 1 ÷ 3 leaves remainder 1.

• 4 ÷ 3 leaves remainder 1.

• 7 ÷ 3 leaves remainder 1.

• 10 ÷ 3 leaves remainder 1.

Answer: 1, 4, 7, 10, 13, ...

Common difference = 4 − 1 = 3.

Q7. Write the sequence of natural numbers whose last digit is 1 or 6 in ascending order. Describe this sequence in two other ways.

Solution:

The natural numbers ending in 1 or 6 are:

1, 6, 11, 16, 21, 26, ...

Two other ways to describe this sequence are:

1. These are natural numbers that leave a remainder of 1 when divided by 5.

2. This is an arithmetic sequence with a common difference of 5.

Answer: 1, 6, 11, 16, 21, 26, ...

Q8. In the given triangular pattern, how many red triangles are there in each picture?

Solution:

From the given figures:

• First picture = 3 red triangles

• Second picture = 9 red triangles

• Third picture = 27 red triangles

Each new picture has three times the number of red triangles in the previous picture.

Answer: 3, 9, 27, ...

Q9. If the area of the original uncut triangle is taken as 1, calculate the area of one small triangle in each of the three pictures.

Solution:

From the given triangular figures:

• First picture = 1/4

• Second picture = 1/16

• Third picture = 1/64

Each successive small triangle has one-fourth the area of the previous small triangle.

Answer: 1/4, 1/16, 1/64, ...

Q10. Check whether the sequence of half of the odd natural numbers is an arithmetic sequence. Find its common difference.

Solution:

The odd natural numbers are:

1, 3, 5, 7, 9, ...

Taking half of each number gives:

1/2, 3/2, 5/2, 7/2, 9/2, ...

Now, calculate the difference between consecutive terms:

3/2 − 1/2 = 1

5/2 − 3/2 = 1

7/2 − 5/2 = 1

The difference between consecutive terms is constant.

Answer: Yes, it is an arithmetic sequence, and its common difference is 1.

Kerala SSLC Maths Chapter 1 Important Questions PDF Download

Students can download the Kerala SSLC Maths Chapter 1 Important Questions PDF to practise key problems from Arithmetic Sequences along with their solutions. Refer to the Kerala SSLC Maths Syllabus to understand the topics included in the examination. The PDF provides a convenient way to revise important questions and practise problem-solving before the board exams.

How to Use Important Questions for Kerala Class 10 Maths Arithmetic Sequences for Exam Preparation

A planned preparation strategy helps students understand concepts and practise effectively for the Kerala SSLC examination. Students should also check the Kerala SSLC Exam Pattern to understand the question format and marking scheme. Follow these steps to make the best use of the important questions and solutions.

• Master Basic Formulas: Revise the formulas for the nth term and sum of terms before attempting the questions. Practise applying these formulas to different arithmetic sequences.

• Solve Questions Independently: Attempt each problem on paper before checking the final answer. This helps improve calculation speed and accuracy.

• Identify Common Difference: Focus on finding the first term and common difference correctly in every sequence.

• Check Doubtful Steps: Use the solutions to identify algebraic errors and improve your problem-solving approach.

• Follow the Exam Schedule: Check the Kerala SSLC Exam Time Table to plan your revision and allocate sufficient time to practise Mathematics before the examination.

• Practise Previous Papers: Solve previous years' question papers to understand question patterns and improve time management.

Practising Kerala SSLC Maths Chapter 1 Important Questions helps students strengthen their understanding of Arithmetic Sequences and improve problem-solving skills. Regular revision of formulas, solving different question types, and practising previous years' papers can help students prepare confidently for the Kerala SSLC examination.