1. Arithmetic & Geometric Sequences

2. Definition Arithmetic Sequence
If a sequence of values follows a pattern of adding a fixed amount from one term to the next, it is referred to as an  arithmetic sequence.
General Rule
an = a1 + (n – 1)d
a1 is the first term and d is the common difference.

8. Definition Geometric Sequence
A geometric sequence is a sequence where each term is found by multiplying or dividing the same value from one term to the next. We call this value "common ratio"
General Rule
an = a1 (r)n-1
a1 is the first term & r is the common ratio

13. 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

14. 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

15. 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

16. 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

17. Let’s Practice!