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Kerala Syllabus 10th Standard Maths Solutions
Chapter 1 Arithmetic Sequences
July 5, 2022 by Prasanna
You can Download Arithmetic Sequences Questions and Answers, Activity, Notes,
Kerala Syllabus 10th Standard Maths Solutions Chapter 1 help you to revise complete
Syllabus and score more marks in your examinations.
Kerala State Syllabus 10th Standard Maths Solutions
Chapter 1 Arithmetic Sequences
Arithmetic Sequences Text Book Questions and Answers
Textbook Page No. 10
Arithmetic Sequence Questions And Answers 10th Standard Question 1.
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, ………
Sum of inner angles
Sum of outer angles
One inner angle
One outer angle
Arithmetic Sequence worksheet with Answer:
No. of triangles of a regular polygon having no. of sides are 3, 4, 5 ………… n respectively
is given as 1, 2, 3, 4. Sum of interior angles of a triangle is 180°.
Then the sequence of Sum of interior angles
= 180, 180 × 2, 180 × 3 …. = 180, 360, 540, ……………….
Sum of exterior angles of any geometric structure having any number of sides is
always 360°.
Sum of exterior angles = 360, 360, …………..
,One interior angle
= 360
3
, 360
4
, 360
5
, ……………. = 120, 90, 72, ………….
Find the sequence calculator can determine the terms (as well as the sum of all terms)
of the arithmetic, geometric, or Fibonacci sequence.
Arithmetic Sequence Class 10 Kerala Syllabus Question 2.
Look at these triangles made with dots. How many dots are there in each ?
Compute the number of dots needed to make the next three triangles.
Arithmetic Sequence worksheet with Answer:
3, 6, 10
The number of dots needed to make the next three triangles will be:
10 + 5 = 15
15 + 6 = 21
21 + 7 = 28
15, 21, 28 Dots
Arithmetic Sequence Question 3.
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.
Answer:
The numbers that leave 1 as remainder when divided by 3 are 1, 4, 7, 10, 13, ………..
(Sequence each with difference of 3 and starting from 1)
The numbers that leave 2 as remainder when divided by 3 are 2, 5, 8, 11, 14, ………….
( Sequence each with difference of 3 and starting from 2)
Kerala Syllabus 10th Standard Maths Chapter 1 Question 4.
Write down the sequence of natural numbers ending in 1 or 6 and describe it in two
other ways.
Answer:
1, 6, 11, 16, 21, ……………..
Numbers, each with difference of 5 and starting from 1.
Numbers, when divided by 5, leaves 1 as remainder.
SSLC Maths Arithmetic Sequence Question 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.
,Answer:
Water in the tank initially = 1000 litre
Water in the tank after first second
= 1000 – 5 = 995 litre
Water in the tank after next second
= 995 – 5 = 990 litre
Water in the tank after third second
= 990 – 5 = 9.85 litre
Sequence 1000, 995, 990, 985, 980, ………………
Textbook Page No. 15
Sslc Maths Chapter 1 Question Answer Question 1.
Write the algebraic expression for each of the sequences below:
i. Sequence of odd numbers
ii. Sequence of natural numbers which leave remainder 1 on division by 3.
iii. The sequence of natural numbers ending in 1.
iv. The sequence of natural numbers ending in 1 or 6.
Answer:
i. Sequence of odd numbers = 1, 3, 5, 7 …………
That is 2 × 1 – 1,2 × 2 – 1,
Common difference a = 2,
First term, a + b=1, b = 1
Algebraic expression xn = an + b = 2n – 1
n=1, 2, 3 ………..
ii. Sequence of natural numbers which leave remainder 1 on division by 3.
1, 4, 7, 10, 13, 16
x1 = 1
x2 = 1 + 3(1) = 4
x3 = 1 + 3(2) = 7
………………………
……………………..
xn= 1 + 3(n – l) = 3n – 2
Algebraic expression xn = 3n – 2
n = 1, 2, 3 …………..
iii. The sequence of natural numbers ending in 1 is 1, 11, 21, 31……….
That is 10 × 1 – 9, 10 × 2 – 9, ……………….
Algebraic expression xn = 10n – 9
n = 1,2,3 ………….
, iv. The sequence of natural numbers ending in 1 or 6 is 1, 6, 11, 16, 21 ………….
That is 5 × 1 – 4, 5 × 2 – 4,
Algebraic expression xn = 5n – 4
n=1,2,3 ……………….
An arithmetic common difference calculator is an online free tool to find the arithmetic
sequence with the given common difference.
Arithmetic Sequence Pictures Question 2.
For the sequence of regular polygons starting with an equilateral triangle, write the
algebraic expressions for the sequence of the sums of inner angles, the sums of the
outer angles, the measures of an inner angle, and the measure of an outer angle.
Answer:
Let n be the number of sides
Sum of interior angles: 180°, 360°, 540°, 720°, ……………
Algebraic expression xn = 180n
Sum of exterior angles 360°, 360°, 360°,………..
Algebraic expression xn = 360°
Sequence of one interior angle:
180° 360° 540°
3
, 4
, 5
………………
0
Algebraic expression xn = 180 n
n+2
Sequence of one exterior angle:
360°
3
, 360°
4
, 360°
5
, …………..
0
360
Algebraic expression xn = = n+2
Class 10 Maths Chapter 1 Kerala Syllabus Question 3.
Look at these pictures:
The first picture is got by removing the small triangle formed by joining the midpoints
of an equilateral triangle. The second picture is got by removing such a middle triangle
from each of the red triangles of the first picture. The third picture shows the same
thing done on the second.
i. How many red triangles are there in each picture?
ii. Taking the area of the original uncut triangle as 1, compute the area of a small
triangle in each picture.
iii. What is the total area of all the red triangles in each picture?
HSSLive Guru
Kerala Syllabus 10th Standard Maths Solutions
Chapter 1 Arithmetic Sequences
July 5, 2022 by Prasanna
You can Download Arithmetic Sequences Questions and Answers, Activity, Notes,
Kerala Syllabus 10th Standard Maths Solutions Chapter 1 help you to revise complete
Syllabus and score more marks in your examinations.
Kerala State Syllabus 10th Standard Maths Solutions
Chapter 1 Arithmetic Sequences
Arithmetic Sequences Text Book Questions and Answers
Textbook Page No. 10
Arithmetic Sequence Questions And Answers 10th Standard Question 1.
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, ………
Sum of inner angles
Sum of outer angles
One inner angle
One outer angle
Arithmetic Sequence worksheet with Answer:
No. of triangles of a regular polygon having no. of sides are 3, 4, 5 ………… n respectively
is given as 1, 2, 3, 4. Sum of interior angles of a triangle is 180°.
Then the sequence of Sum of interior angles
= 180, 180 × 2, 180 × 3 …. = 180, 360, 540, ……………….
Sum of exterior angles of any geometric structure having any number of sides is
always 360°.
Sum of exterior angles = 360, 360, …………..
,One interior angle
= 360
3
, 360
4
, 360
5
, ……………. = 120, 90, 72, ………….
Find the sequence calculator can determine the terms (as well as the sum of all terms)
of the arithmetic, geometric, or Fibonacci sequence.
Arithmetic Sequence Class 10 Kerala Syllabus Question 2.
Look at these triangles made with dots. How many dots are there in each ?
Compute the number of dots needed to make the next three triangles.
Arithmetic Sequence worksheet with Answer:
3, 6, 10
The number of dots needed to make the next three triangles will be:
10 + 5 = 15
15 + 6 = 21
21 + 7 = 28
15, 21, 28 Dots
Arithmetic Sequence Question 3.
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.
Answer:
The numbers that leave 1 as remainder when divided by 3 are 1, 4, 7, 10, 13, ………..
(Sequence each with difference of 3 and starting from 1)
The numbers that leave 2 as remainder when divided by 3 are 2, 5, 8, 11, 14, ………….
( Sequence each with difference of 3 and starting from 2)
Kerala Syllabus 10th Standard Maths Chapter 1 Question 4.
Write down the sequence of natural numbers ending in 1 or 6 and describe it in two
other ways.
Answer:
1, 6, 11, 16, 21, ……………..
Numbers, each with difference of 5 and starting from 1.
Numbers, when divided by 5, leaves 1 as remainder.
SSLC Maths Arithmetic Sequence Question 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.
,Answer:
Water in the tank initially = 1000 litre
Water in the tank after first second
= 1000 – 5 = 995 litre
Water in the tank after next second
= 995 – 5 = 990 litre
Water in the tank after third second
= 990 – 5 = 9.85 litre
Sequence 1000, 995, 990, 985, 980, ………………
Textbook Page No. 15
Sslc Maths Chapter 1 Question Answer Question 1.
Write the algebraic expression for each of the sequences below:
i. Sequence of odd numbers
ii. Sequence of natural numbers which leave remainder 1 on division by 3.
iii. The sequence of natural numbers ending in 1.
iv. The sequence of natural numbers ending in 1 or 6.
Answer:
i. Sequence of odd numbers = 1, 3, 5, 7 …………
That is 2 × 1 – 1,2 × 2 – 1,
Common difference a = 2,
First term, a + b=1, b = 1
Algebraic expression xn = an + b = 2n – 1
n=1, 2, 3 ………..
ii. Sequence of natural numbers which leave remainder 1 on division by 3.
1, 4, 7, 10, 13, 16
x1 = 1
x2 = 1 + 3(1) = 4
x3 = 1 + 3(2) = 7
………………………
……………………..
xn= 1 + 3(n – l) = 3n – 2
Algebraic expression xn = 3n – 2
n = 1, 2, 3 …………..
iii. The sequence of natural numbers ending in 1 is 1, 11, 21, 31……….
That is 10 × 1 – 9, 10 × 2 – 9, ……………….
Algebraic expression xn = 10n – 9
n = 1,2,3 ………….
, iv. The sequence of natural numbers ending in 1 or 6 is 1, 6, 11, 16, 21 ………….
That is 5 × 1 – 4, 5 × 2 – 4,
Algebraic expression xn = 5n – 4
n=1,2,3 ……………….
An arithmetic common difference calculator is an online free tool to find the arithmetic
sequence with the given common difference.
Arithmetic Sequence Pictures Question 2.
For the sequence of regular polygons starting with an equilateral triangle, write the
algebraic expressions for the sequence of the sums of inner angles, the sums of the
outer angles, the measures of an inner angle, and the measure of an outer angle.
Answer:
Let n be the number of sides
Sum of interior angles: 180°, 360°, 540°, 720°, ……………
Algebraic expression xn = 180n
Sum of exterior angles 360°, 360°, 360°,………..
Algebraic expression xn = 360°
Sequence of one interior angle:
180° 360° 540°
3
, 4
, 5
………………
0
Algebraic expression xn = 180 n
n+2
Sequence of one exterior angle:
360°
3
, 360°
4
, 360°
5
, …………..
0
360
Algebraic expression xn = = n+2
Class 10 Maths Chapter 1 Kerala Syllabus Question 3.
Look at these pictures:
The first picture is got by removing the small triangle formed by joining the midpoints
of an equilateral triangle. The second picture is got by removing such a middle triangle
from each of the red triangles of the first picture. The third picture shows the same
thing done on the second.
i. How many red triangles are there in each picture?
ii. Taking the area of the original uncut triangle as 1, compute the area of a small
triangle in each picture.
iii. What is the total area of all the red triangles in each picture?
