1. Sequences and Series
Arithmetic series.

2. Sequence
Series
List with commas.
Indicated sum,
addition of terms.
3, 8, 13, 18

3. Arithmetic Series

4. The sum of the first n terms of an arithmetic series is given by the formula:
Example 1. Find the sum of the first 20 terms of the arithmetic sequence 3, 13, 23, …..

5. .
Example 2
Find the sum of the first 30 terms of an arithmetic sequence with first term 64 and common difference -3.

6. Example

7. Your turn!
Find the sum of the first 25 terms of an arithmetic series …
or sum(seq(105-5n,n,1,25)

8. Example 3. A new business is selling computers
Example 3. A new business is selling computers. They predict to sell 20 computers in their first month, 23 in the 2nd, 26 in the 3rd and so on. How many months will pass before the company expects to sell their thousandth computer?
We know that
nSolve gives n= …
so in their 21st month the sales will reach 1000 computers.

9. Using GDC with sum(seq Example 4
Find the sum of the first 6 terms of an arithmetic sequence with first term 2 and common difference 5.

10. Example
An arithmetic series has first term 10 and a common difference of ¼. Find the least number of terms of the series such that the sum exceeds 300.
In general use polyRoots or graph it. Numerical solve works here as the positive solution is closer to zero but be careful!

11. Write the first three terms and the last two terms of the following arithmetic series.
What is the sum of this series?

12. What is the SUM of these terms?
Written 1st to last.
Written last to 1st.
Add Down
50 Terms
71 + (-27) Each sum is the same.

13. Vocabulary of Arithmetic Sequence and Series
It is important to note in an exam question whether it asks for the nth term or for the sum of the first n terms!

14. Your Turn

15. Ex Qns 1 to 11
Ex Qns 1-7
Ex Qns 2, 4, 7, 9, 11