1. Arithmetic and Geometric Sequences

2. What is an arithmetic sequence?
A sequence in which each term is found by ADDING the same number to the previous term.
4, 8, , 16, 20………….. +4 +4 +4 +4

3. What is the common difference?
The difference between each number. This determines what is added to each previous number to obtain the next number.
4, 8, 12, 16, 20…………..
4 is the common difference

4. What is a geometric sequence?
A sequence in which each term can be found by multiplying the previous term by the same number.
3, 9, , 81, ………….. x3 x3 x3 x3

5. What is the common ratio?
The number used to multiply by each previous number to obtain the next number.
2, 8, 32, 128, 512…………..
4 is the common ratio

6. Let’s Practice!

7. Is this an arithmetic or geometric sequence?
10, 15, 20, 25, 30……
Arithmetic Sequence +5
5 is the common difference

8. Is this an arithmetic or geometric sequence?
2, 12, 72, 432, 2,592……
Geometric Sequence x6
6 is the common ratio

9. What is the next term in this sequence? 5, 20, 80, 320 , _____
1,280

10. What is the next term in this sequence? 5, -1, -7 -13 , _____-6 -6 -6 -6
-19

11. What is the next term in this sequence? -3, 6, -12, 24 , _____
-48

12. What is the next term in this sequence? -400,-380,-360,-340 , ____
+20
+20
+20
+20
-320

13. What is the next term in this sequence? 100, 75, 50 , 25____
-25
-25
-25
-25

14. What is the next term in this sequence? 12, -48, 192 , -768____
3,072

15. LETS PRACTISE

16. Given that arithmetic sequence: 30, 23, 16, 9, 2…… find the 15th term and the sum of the first 15 terms
2. The first three terms of a sequence are 2, b, 18. Find the positive value of b so that the sequence is
a. An arithmetic progression
b. A geometric progression
3. Given a, a+1, a-2 are three consecutive terms of a geometric sequence, find the value of y and the common ratio.

17. 4. The first term of an arithmetic sequence is -8 and the last term is 70. If the common different is 5 find
a. The number of the terms in the sequence
b. The sum of all the terms in the sequence