# SCERT Kerala Maths Class 10/ Arithmetic Sequences – Chapter 1

**SCERT Kerala Maths Class 10/ Arithmetic sequence is about text book solutions of Arithmetic Sequences Chapter 1 of Class 10 Mathematics. Here you can find out text book solutions of the topic Number patterns.**

**Kerala State Syllabus Class 10 Mathematics Text Book Solutions/ SCERT Kerala SSLC Class 10 MathsArithmetic Sequences – Chapter 1/ Part 1**

—————————————————————————————————————————————-**Number Patterns:**

Answer the following questions:

Find the perimeter of a square of sides 1 cm, 2 cm, 3cm, and 4cm. Also find their areas and write as a sequence.

Solution:

Perimeter of a square = 4 x side

Perimeter of a square of side 1 cm = 4 x 1 = 4 cm

Perimeter of a square of side 2 cm = 4 x 2 = 8 cm

Perimeter of a square of side 3 cm = 4 x 3 = 12 cm

Perimeter of a square of side 4 cm = 4 x 4 = 16 cm

So the perimeters form the multiples of 4, in order 4, 8, 12, 16—————–

Now we can find out its areas.

Area of a square = side x side

Area of a square of side 1 cm = 1 x 1 = 1 square cm

Area of a square of side 2 cm = 2 x 2 = 4 square cm

Areas of a square of side 3 cm = 3 x 3 = 9 square cm

Area of a square of side 4 cm = 4 x 4 = 16 square cm

The areas form the perfect squares in order 1, 4, 9, 16 —————

- Make the following number sequences, from the sequence of equilateral triangles, squares, regular pentagons and so on, of regular polygons:

Number of sides: 3, 4, 5 ———

a) Sum of inner angles:

b) Sum of outer angles:

c) One inner angle

d) One outer angle

Solution:

a) Sum of the interior angles of a polygon with n sides = (n – 2) x 180 degree

Sum of the interior angles of a polygon with 3 sides = (3 – 2) x 180 = 1 x 180 = 180 degree

Sum of the interior angles of a polygon with 4 sides = (4 – 2) x 180 = 2 x 180 = 360 degree

Sum of the interior angles of a polygon with 5 sides = (5- 2) x 180 = 3 x 180 = 540 degree

So the required number sequence is 180, 360, 540, ———-

b) The sum of the measures of the external angles of any polygon is 360 degree.

So the required number sequence is 360, 360, 360 ————–

c) For an equilateral triangle, all inner angles are 60 degree each.

For a square, all inner angles are of 90 degree each.

For a regular pentagon, all inner angles are of 108 degree each.

So the required number sequence is 60, 90, 108, ——–

d) Sum of outer angles of any polygon is 360 degree.

So one outer angle of an equilateral triangle is 360/3 = 120 degree

For a square 360/ 4 = 90 degree

For a regular pentagon 360/5 = 72 degree

So the required number sequence is 120, 90, 72…………… - Look at these triangles made with dots. (For picture, look at the text book)

How many dots are there in each? Compute the number of dots needed to make the next three triangles?

Solution:

3,6,10 dots are there in the given picture.

The number of dots needed to make the next three triangles will be

10 + 5 = 15

15 + 6 = 21

21 + 7 = 28 - Write down the sequence of natural numbers leaving remainder 1 on division by 3 and the sequence of natural numbers leaving remainder 2 on division by 3.

Solution:

The sequences of natural numbers leaving remainder 1 on division by 3 are 1, 4, 7, 10, 13 —-

The sequences of natural numbers leaving remainder 2 on division by 3 are 2, 5, 8, 11, 14—- - Write down the sequence of natural numbers ending in 1 or 6 and describe it in two other ways.

Solution:

The sequences of natural numbers ending in 1 or 6 are 1, 6, 11, 16, 21, 26 ———-

We can write this as 1, 1 + 5, 6 + 5, 11 + 5, 16 + 5, 21 + 5, ————— OR

Numbers, leaving remainder 1 on division by 5. - A tank contains 1000 litres of water and it flows out at the rate of 5 litres per second. How much water is there in the tank after each second? Write their numbers as a sequence.

Solution:

Quantity of water in the tank = 1000 litre

Water in the tank after 5 seconds = 1000 – 5 = 995 litre

Water in the tank after next 5 seconds = 995 – 5 = 990 litre

Water in the tank after next 5 seconds = 990 – 5 = 985 litre

So the required number sequence is 1000, 995, 990, 985, 980, ————————–