Question

Look at the number pattern given below.

1

2 3 4

5 6 7 8 9

10 11 12 13 14 15 16

..................................................................................

............................................................................................................

a) Write the next two more lines of this pattern ?

b) How many numbers are there in the 9th line?



c) What is the last number in the 9th line ?

d) What is the the first term in the 11th line ?​

Answer 1

Answer:

A (i)=17,18,19,20,21,22,23,24,25,

(ii)= 26,27,28,29,30,31,32,33,34,35,36

B = 17

Answer 2

Given:  

$1\\2,3,4\\5,6,7,8,9,\\10,11,12,13,14,15,16$

To find:

• The next two lines
• Numbers in the eleventh line
• last number in the ninth line
• The first term in the 11th line

Step-by-step explanation:

• Here we need to find the pattern. We can see that the numbers in the line are increasing according to the prime numbers.

Solution:

Hence, the difference between the numbers in the lines is according to the rime numbers.

writing the whole lines.

$1\\2,3,4\\5,6,7,8,9\\10,11,12,13,14,15,16\\17,18,19,20,21,22,23,24,25,26,27\\28,29,30,31,32,33,34,35,36,37,38,39,40$

Now numbers in the ninth line will be

In the sixth line we have $13$ numbers. Therefore, according to the prime numbers we will have:

 

$6th = 13\\7th = 17\\8th =19\\9th = 23$

Hence, the ninth line will have $23$ numbers.

Now, the last number of the ninth line:

We will add the last number of 6th lines for 9th

$40 +17 = 57\\57 +19 = 76\\76 + 23 = 99$

Hence, the last number of the ninth line will be $99$

Now, the first term in the eleventh line will be

$10th = 29\\11th =31$

So the eleventh line will have $31$ numbers

So adding numbers:

$99+29 = 128$

The first number will be obtained by adding one to it:

$128+1=129$

Hence, $129$ is the first term for the eleventh line