8. Recursive Formulas
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The given rule means that, after the first term of the sequence, every term a_n is the difference between the previous term a_(n-1) and 3.
16, 13, 10, 7, and 4
a_1&=16 a_n&=a_(n-1)-3, for n ≥ 2 To do so, we will use a table.
| n | a_n=a_(n-1)-3 | a_(n-1)-3 | a_n |
|---|---|---|---|
| 1 | a_1=16 | - | 16 |
| 2 | a_2=a_(2-1)-3 | a_1-3= 16-3 | 13 |
| 3 | a_3=a_(3-1)-3 | a_2-3= 13-3 | 10 |
| 4 | a_4=a_(4-1)-3 | a_3-3=10-3 | 7 |
| 5 | a_5=a_(5-1)-3 | a_4-3=7-3 | 4 |
Therefore, the first 5 terms of the sequence are 16, 13, 10, 7, and 4.