The given rule means that, after the first term of the sequence, every term a_n is the product between the previous term a_(n-1) and - 3.
Terms: - 4, 12, - 36, 108, - 324, and 972 Graph:
Practice makes perfect
We are asked to write the first 6 terms of a sequence and to graph them.
Writing the First 6 Terms
Let's find the terms, given a recursive rule.
a_1&=- 4
a_n&=- 3a_(n-1), for n>1To do so, we will use a table.
n
a_n=- 3a_(n-1)
- 3a_(n-1)
a_n
1
a_1=- 4
-
- 4
2
a_2=- 3a_(2-1)
- 3( a_1)=- 3( - 4)
12
3
a_3=- 3a_(3-1)
- 3( a_2)=- 3( 12)
- 36
4
a_4=- 3a_(4-1)
- 3(a_3)=- 3(- 36)
108
5
a_5=- 3a_(5-1)
- 3(a_4)=- 3(108)
- 324
6
a_6=- 3a_(6-1)
- 3(a_5)=- 3(- 324)
972
Therefore, the first 6 terms of the sequence are - 4, 12, - 36, 108, - 324, and 972.
Graphing the Sequence
To graph the first six 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.
