Class 6 Maths Chapter 1 Extra Questions Patterns in Mathematics
Class 6 Maths Patterns in Mathematics Extra Questions
NCERT Class 6 Maths Chapter 1 Patterns in Mathematics Extra Questions and Answers
Very Short Answer Type Questions
Question 1.
What is the next number in the sequence 3, 6, 9,12 … ?
Answer:
We have, the sequence 3, 6, 9, 12, …
Here, the sequence is the multiple of 3.
∴ The next number is 15.
Question 2.
What shape comes next in this pattern?
Answer:
The next shape in the pattern
Question 3.
Continue the pattern : 2, 4, 6,…
Answer:
We have, 2, 4,6,…
The next terms in the given pattern are 8, 10, 12, …
Thus, the sequence is 2, 4, 6, 8, 10,…
Question 4.
What is the next number in the sequence
1, 2, 4, 8,… ?
Answer:
We have, 1, 2, 4, 8,… v
Here, the sequence is the powers of 2.
∴ Next number is 16.
Question 5.
What comes next in the sequence 5, 10, 15,…?
Answer:
We have, 5,10,-15,…
Here, the sequence is the multiple of 5.
∴ Next number in the sequence is 20.
Short Answer Type Questions
Question 1.
Identify the appropriate rule for the given sequences,
(i) 5,10,15, 20,…
(ii) 2, 6,10, 14,…
Answer:
(i) Sequence is the multiple of 5.
(ii) Sequence has the difference of 4 between consecutive two terms.
Question 2.
Write the next three terms for the following sequences,
(i) 3, 8,13,18,…
(ii) 10, 20, 30, 40,…
(iii) 4, 8, 12, 16,…
Answer:
(i) 23, 28, 33
(ii) 50, 60, 70
(iii) 20, 24, 28
Question 3.
Give the pictorial representation of the number
Sequence 3, 6, 9, 12, …
Answer:
We have, 3, 6, 9, 12,…
Question 4.
You will have noticed that 9 is both an odd number and a square number. Make pictures in your notebook illustrating this.
Answer:
Question 5.
Which sequence do you get when yoti start to add all 2’s sequence up?
Answer:
2, 4, 6, 8,…
Question 6.
Which sequence do you get when you start to add two consecutive even numbers minus 1?
Answer:
5, 9, 13, 17,…
Question 7.
What is the 4th shape in a pattern when we starts with a triangle and the number of sides increases by 1 with each Shape?
Answer:
Hexagon
Question 8.
If a shape sequence starts with a triangle and each subsequent shape adds one more side (triangle,, square, pentagon etc.), how many sides does 5th Shape have?
Answer:
7
Question 9.
Identify the polygon according to the number of sides.
Answer:
3 – Triangle
6 – Hexagon
9 – Nonagon
10 – Decagon
Question 10.
Find the next two numbers in the sequence
1, 4, 9, 16, ……………….
Answer:
We have, 1, 4, 9, 16,…
Here, the sequence is square.
∴ The next two numbers are 25, 36.
Question 11.
What is the 7th number in the sequence
5, 10, 15, 20,……… ?
Answer:
We have, 5, 10, 15,20,…
Here, the sequence is the multiple of 5.
∴ The 7th number in the sequence is 35.
Question 12.
Create a pattern using the rule ‘Add 5 to the previous number’ starting with 2.
Answer:
First number is 2.
Add 5 to the 2
i.e. 2 + 5 = 7
7 + 5 = 12
12 + 5 = 17
17 + 5 = 22
∴ Required pattern is 2, 7, 12, 17, 22,…
Question 13.
If the pattern is 1, 3, 5, 7, ……………. what is the 10th number in the sequence?
Answer:
We have, 1, 3, 5,7,…
Here, it is the sequence of odd numbers.
∴ The 10th number is 19.
Question 14.
What is the rule in this sequence
100, 90, 80, 70, ………?
Answer:
We have, 100, 90, 80, 70,…
Here, next term is 10 less than the previous number.
Question 15.
A staircase is built where each step is made with blocks increasing by one (1 block, 2 blocks, 3 blocks, etc.). How many blocks are needed for the 6th step?
Answer:
We have, the staircase in the pattern 1, 2, 3, …
∴ Number of blocks needed for the 6th step is 6.
Long Answer Type Questions
Question 1.
A gardener plants flowers in rows of 2, 4, 6, 8 and so on. How many flowers will be in the 8th row?
Answer:
We have, the flowers in the pattern 2,4, 6, 8, …
Number of flowers in the 8th row will be 16.
Question 2.
If a bakery arranges cookies in rows of 1, 4, 9,16, and so on, how many cookies will be in the 7th row?
Answer:
We have, cookies arranged in the sequence 1, 4, 9, 16,…
∴ Number of cookies in the 7th row will be 49.
Question 3.
Imagine you are filling a jar with marbles. Each time, you add 3 more marbles than before. If you start with 2 marbles, how many marbles will you have after 5 rounds?
Answer:
We have, 2 marbles.
Next jar will have 3 marbles more than the previous jar.
∴ The sequence is 2, 5, 8,11, …
Hence, number of marbles after 5 rounds
= 2 + 5 + 8 + 11 + 14
= 40
Question 4.
In a parking lot, the number of cars parked increases by 7 each hour (7,14, 21,…). How many cars will be parked after 8 hours?
Answer:
We have, the sequence, 7, 14, 21,…
Which shows number of cars parked increases by 7 each hour.
∴ Number of cars parked after 8 h = 56
Question 5.
What happens when you start to add up powers of 3 starting with 1, i.e. take 1, 1 + 3, 1 + 3 + 9, 1 + 3 + 9 + 27, … ?
Answer:
Adding up powers of 3 starting with 1.
1 = 1
1 + 3 = 3
1 + 3 + 9 = 13
1 + 3 + 9 + 27 = 40
1 + 3 + 9 + 27 + 81 = 121
Case Based Questions
Question 1.
A gardener is planning a flower garden. She decides to plant the flowers in rows where the number of flowers in each row follows a pattern.
Based on the above information, answer the following questions.
(i) In the first row, she plants 2 flowers, in the second row 4 flowers, and in the third row 6 flowers. If she “ continuous this pattern, how many flowers will be . in the 7th row?
(a) 14
(b) 10
(c) 12
(d) 8
Answer:
(a) 14
According to the given condition, she plants 2 more plants in the next row from the previous row.
The sequence of plants is as follows:
2,4, 6, 8, 10, 12, 14, 16,…
So, number of plants in the 7th row will be 14.
(ii) How many total flowers will she have planted by the time she finishes the 5th row?
(a) 10
(b) 20
(c) 30
(d) 40
Answer:
(c) 30
Total number of flowers till 5th row = 2 + 4 + 6 + 8 + 10 = 30
(iii) If the pattern changes after the 5th row, so that each subsequent row has one less flower than the previous row, how many flowers will be in the 10th row?
(a) 7
(b) 5
(c) 6
(d) 8
Answer:
(b) 5
According to the given condition, after 5th row, each subsequent row has one less flower than the previous one, i.e. 2, 4, 6, 8, 10, 9, 8, 7, 6, 5,…
∴ Number of flowers in the 10th row will be 5.
Question 2.
A builder is constructing a wall using bricks. He starts by placing 1 brick in the first row, 3 bricks in the second row, and 5 bricks in the third row.
Based oh the above information, answer the following questions.
(i) If this pattern continuous, how many bricks will be in the 6th row?
(ii) How many bricks are needed to build the wall up to the 7th row?
Answer:
(i) According to the given condition, we have the sequence, 1, 3, 5,…
Which is an odd number sequence
∴ Number of bricks in the 6th row will be 11.
(ii) Number of bricks needed to build the wall up to 7th row will be 49 (i.e. 7²).
Skill Based Questions
Question 1.
Across
1. A polygon which has all its sides equal and so all angles are equal is called polygon.
2. 1, 2, 3, 4 …………. are called ____ numbers.
3. 2, 4, 6, 8, 10, 12 …….. are called ____ numbers.
4. 1, 3, 6, 10, 15, 21 ……….. are called ____ numbers.
Down
1. 1, 4, 9,16, 25, ………. are called ____
2. 1, 8, 27, 64, 125 ……. called ____
3. On adding the counting numbers up and down, we get the sequence of ____ numbers.
4. 0, 1, 2, 3, 4 …………. is the sequence of ____ numbers.
Answer:
Across
1. Regular
2. Counting
3. Even
4. Triangular
Down
1. Squares
2. Cube
3. Square
4. Whole