Page 19 - NUMINO Challenge_B2
P. 19
2 Addition by Grouping
Basic Concepts Sum of Consecutive Numbers
The sum of consistently increasing numbers can be found using the simple
equation below.
123456789
{(First number) (Last number)} (Number of Numbers) 2
Find the sum of consecutive numbers from 1 to 9.
123456789
987654321
10 10 10 10 10 10 10 10 10
9 terms 90 2 45
10 9 90,
When expressed as an equation, the sum of consecutive numbers is:
123 9 (1 9) 9 2 45
This method is called Gauss’s Addition Formula, named after its inventor.
Example Find the sum of consecutive numbers from 1 to 99.
1234 98 99
Class Notes 971 981 991
31 21 11
Add the consecutive numbers twice as shown below.
11 21 31 41 51
991 981 971 961 951
terms
Since the result of adding consecutive numbers from 1 to 99 twice is equal to adding
to itself times, .
Therefore, the sum of consecutive numbers from 1 to 99 is 2.
Try It Again Find the sum of the following consecutive numbers.
1234 68 69 70
16 NUMINO Challenge B2
Basic Concepts Sum of Consecutive Numbers
The sum of consistently increasing numbers can be found using the simple
equation below.
123456789
{(First number) (Last number)} (Number of Numbers) 2
Find the sum of consecutive numbers from 1 to 9.
123456789
987654321
10 10 10 10 10 10 10 10 10
9 terms 90 2 45
10 9 90,
When expressed as an equation, the sum of consecutive numbers is:
123 9 (1 9) 9 2 45
This method is called Gauss’s Addition Formula, named after its inventor.
Example Find the sum of consecutive numbers from 1 to 99.
1234 98 99
Class Notes 971 981 991
31 21 11
Add the consecutive numbers twice as shown below.
11 21 31 41 51
991 981 971 961 951
terms
Since the result of adding consecutive numbers from 1 to 99 twice is equal to adding
to itself times, .
Therefore, the sum of consecutive numbers from 1 to 99 is 2.
Try It Again Find the sum of the following consecutive numbers.
1234 68 69 70
16 NUMINO Challenge B2
