In this lesson, we learned how to identify the two different types of sequences, arithmetic and geometric, and how to find a formula for its nth term.
- arithmetic sequence: a sequence that is generated by adding the same number each time
-formula: tn= t1 + (n-1)d; t1= 1st term, n= term #, d= difference(what's being added), and tn= _term
- geometric sequence: a sequence that's generated by multiplying the same number each time *to divide, we use fractions (/2 = x 1/2)
-formula: tn= t1 x r^(n-1); t1= 1st term, r= what's being multiplied, n= term #, and
tn= _term
Example 1: Is the following an arithmetic or geometric? 3, 5, 7, ...; Find the formula for the nth term.
-It's arithmetic because you're just adding two to each number.
-tn= t1 + (n-1)2
= 3 + (n-1)2
= 3 + 2n - 2
= 2n +1
Example 2: For tn= 5n + 2, find the first 4 terms and state if it's arithmetic or geometric.
1) 5(1) + 2 = 7
2) 5(2) + 2 = 12
3) 5(3) + 2 = 17
4) 5(4) + 2 = 22
-It's arithmetic because you can see that 5 is being added to each number.
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