WYDOWN MATH CLUB
Arithmetic Sequence
What is an arithmetic sequence?
A common math question is to find the sum of an arithmetic sequence.
Example 1:
Find the sum of the first 5 consecutive integers.
Method 1: Simply add the numbers.
Sum =
Method 2:
5 consecutive integers
Reverse the order:
Sum of the two rows:
:
5
6
1
4
6
2
3
6
3
2
6
4
1
6
5
Find the sum of the third row; what is the relationship to this sum and the sum found using method 1?
Why do you think this is true? What could you do to make the sum in row three to be the sum of the
first five digits?
Example 2:
Find the sum of the first 10 consecutive integers.
Method 1: Simply add the numbers.
Method 2:
10 consecutive integers:
Reverse the order:
Sum of the two rows:
1
10
2
9
3
8
4
7
Sum =
5
6
6
5
7
4
8
3
9
2
10
1
Find the sum of the third row; what is the relationship to this sum and the sum found using method 1?
Why do you think this is true? What could you do to make the sum in row three to be the sum of the
first five digits?
Example 3:
Find the sum of the multiples of 3 starting with 3 and ending with 18.
Method 1: Simply add the numbers.
Method 2:
Sum =
Do you think method two will work for this arithmetic sequence?
Multiples of 3:
Reverse the order:
Sum of the two rows:
3
18
6
15
9
12
12
9
15
6
18
3
Use the procedure (method 2) you developed in example 1 and 2 to find the sum.
Example 4:
Find the sum of the first 100 consecutive integers.
Write a verbal description summarizing how to find the sum of an arithmetic sequence using method 2.
Example 5:
Given the arithmetic sequence {n, n + 5, and n + 10} show that the two methods produce the same sum.
How many zeros are at the end of: 1 • 2 • 3 • 4 • 5 •……• 100