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 8.
First Six Terms of the Sequence: 0, - 8, - 16, - 24, - 32, - 40 Graph:
Practice makes perfect
We are asked to write the first 6 terms of a sequence, given a recursive rule.
a_1&=0
a_n&=a_(n-1)-8To do so, we will use a table.
n
a_n=a_(n-1)-8
a_(n-1)-8
a_n
1
a_1=0
-
0
2
a_2=a_(2-1)-8
a_1-8= 0-8
- 8
3
a_3=a_(3-1)-8
a_2-8= - 8-8
- 16
4
a_4=a_(4-1)-8
a_3-8= - 16-8
- 24
5
a_5=a_(5-1)-8
a_4-8= - 24-8
- 32
6
a_6=a_(6-1)-8
a_5-8= - 32-8
- 40
Therefore, the first 6 terms of the sequence are 0, - 8, - 16, - 24, - 32, and - 40. To graph the terms, we will let the horizontal axis represent the position of the term within the sequence — this is the domain — and the vertical axis will represent the value of the terms — the range.
