Question

1
2 3
4 5 6
7 8 9 10

(a) Write the next two lines of this pattern
(b) Write the first and last numbers of the 10th line of the pattern.
(c) Find the sum of numbers of the first 10 lines.​

Answer 1

Answer:

1. The next two lines of the pattern is

11 12 13 14 15

16 17 18 19 20 21

2. The first and last numbers of 10th line is 46 and 55

3. The sum of all numbers in first 10 lines are 1540

Solution:

Given, pattern of lines is

1

2 3

4 5 6

7 8 9 10

1) Write the next two lines of the pattern above.

As we can see that, number of natural numbers are increased by 1 to every next new step. And the natural numbers are continued as the elements of pattern.

So, by following above pattern, next two lines will be.

11 12 13 14 15

16 17 18 19 20 21

2) Write the first and the last numbers of the 10th line.

As we observe the pattern, series of first elements is 1 2 4 7 11 16 ….

Above series can also be written as 1 1+1 2+2 4+3 7+4 11+5…..

So the next 4 terms would be 16+6 22+7 29+8 37+9

Then series of first elements is 1 2 4 7 11 16 22 29 37 46.

So, the first element of 10th line is 46 and we know that last element of the line is first element+ line number – 1

last element = 46 + 10 – 1 = 55

So, first element is 46 and last element is 55.

3) Find the sum of all the numbers in the first ten lines.

All numbers in first ten lines will be 1 to 55. So we have to find sum of first 55 natural numbers.

\text { Sum of } 55 \text { numbers }=\frac{55 \times(55+1)}{2}=\frac{55 \times 56}{2}=55 \times 28=1540 Sum of 55 numbers =

2

55×(55+1)

=

2

55×56

=55×28=1540

So, sum of numbers in first ten lines is 1540.

Answer 2

Step-by-step explanation:

a. 1

2 3

4 5 6

7 8 9 10

11 12 13 14 15

b. the first number is 7 , the last number is 10

( 10th line of the pattern )

c. 1+2+3+4+5+6+7+8+9+10= 55

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