- A sequence that is generated by adding the same number each time is called the arithmetic sequence.
- Formula: tn = t1 + (n-1) x d
- d = what is being adding/difference
- tn = blank terms
- t1 = first term
- n = term number
- A sequence that is generated by multiplying the same number each time is called the geometric sequence.
- Formula: tn = t1 x r^(n-1)
- r = what is being multiplied
- n = term number
- tn = blank terms
- t1 = first term
- A sequence is a list of numbers.
Example 1: tn = 6n + 20. What is the sequence? Is it geometric, arithmetic, or neither?
- First thing you need to know is you plug in the number of terms you want to find out for n.
- You are going to find out the first four terms.
- T1 = 6(1) + 20 = 26
- T2 = 6(2) + 20 = 32
- T3 = 6(3) + 20 = 38
- T4 = 6(4) + 20 = 44
- Now we have to find out what is the sequence.
- Each time you are adding 6 to get to the next number so that means it is an arithmetic sequence.
Example 2: tn = 5 x 10^n-1. What is the sequence? Is it geometric, arithmetic, or neither?
- Just like in example one, you have to plug in the number of terms you want to find our for n.
- You are going to find the first four terms again.
- T1 = 5 x 10^1-1 = 5 x 10^0 = 5
- T2 = 5 x 10^2-1 = 5 x 10^1 = 50
- T3 = 5 x 10^3-1 = 5 x 10^2 = 500
- T4 = 5 x 10^4-1 = 5 x 10^3 = 5000
- Now you have to find out the sequence.
- Each time you are multiplying 10 to get to the next number so that means it is an geometric sequence.
- Amber :)
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