1. ARITHMETIC SEQUENCES AND SERIES
Week Commencing Monday 5th October
Learning Intention:
To be able to find the sum of an arithmetic series
Contents:
Sum of an Arithmetic Series Formula
Sum Formula Proof
Using the Sum Formula
Real-Life Problems
Assignment 4

2. ARITHMETIC SEQUENCES AND SERIES Sum of an Arithmetic Series
The sum of the first n terms of a series is generally denoted by Sn.
For arithmetic series there is a formula to work out the sum of the first n terms:
where n is the number of terms
a is the first term
d is the common difference

3. ARITHMETIC SEQUENCES AND SERIES Proof for Sum of an Arithmetic Series
You need to be able to reproduce this proof for the Core 1 examination.

4. ARITHMETIC SEQUENCES AND SERIES
Using the Sum Formula
Example:
Find the sum of the series
… to 20 terms
Solution:
First term, a = 4
Common Difference, d = 5
Number of terms, n = 20
Substitute into formula:

5. ARITHMETIC SEQUENCES AND SERIES
Using the Sum Formula
Example:
Find the sum of the series
… + 158
Solution:
First term, a = 2
Common Difference, d = 4
Number of terms, n = ?
We need to find n before we can find the sum.
Un = Un = a + (n -1)d
158 = 2 + (n – 1)(4)
158 = 2 + 4n – 4
158 = 4n – 2
160 = 4n
40 = n
cont’d on next slide

6. ARITHMETIC SEQUENCES AND SERIES
Using the Sum Formula
Example Continued:
Find the sum of the series
… + 158
Solution Continued:
First term, a = 2
Common Difference, d = 4
Number of terms, n = 40
We can now substitute into the sum formula to give:

7. ARITHMETIC SEQUENCES AND SERIES
Real-Life Problems
Arithmetic Series are used in everyday life to solve problems.
Example:
Ahmed plans to save £250 in the year 2001, £300 in 2002, £350 in 2003, and so on until the year 2020.
Is savings for and arithmetic series with common difference £50.
a. Find the amount he plans to save in 2011
b. Calculate his total planned savings over the 20-year period from 2001 to 2020.
Solution on next slide.

8. ARITHMETIC SEQUENCES AND SERIES
Real-Life Problems
Solution:
a. a = £250 d = £50
From 2001 to 2011 is 11 years which means we want the 11th term in the series.
2011: £250 + (11 – 1)(£50)
= £ (£50)
= £250 + £500
= £750
b. a = £250 d = £50 n = 20

9. ARITHMETIC SEQUENCES AND SERIES
Assignment 4 – Sum of Arithmetic Series
Follow the link for Assignment 4 on Sum of Arithmetic Series in the Moodle Course Area. This is a Yacapaca Activity.
Completed assignments must be submitted by 5:00pm on Monday 12th October.