The given rule means that, after the first term of the sequence, every term a_n is the negative half of the previous term a_(n-1).
First Six Terms: 80, - 40, 20, - 10, 5, - 5/2 Graph:
Practice makes perfect
We are asked to write the first 6 terms of a sequence, given a recursive rule.
a_1&=80
a_n&=- 12a_(n-1)
To do so, we will use a table.
n
a_n=-1/2a_(n-1)
a_n
1
a_1=80
80
2
a_2=-1/2a_(2-1) ⇕ a_2=-1/2 a_1
a_2=-1/2( 80) ⇕ a_2 = - 40
3
a_3=-1/2a_(3-1) ⇕ a_3=-1/2 a_2
a_3=-1/2( - 40) ⇕ a_3=20
4
a_4=-1/2a_(4-1) ⇕ a_4=-1/2a_3
a_4=-1/2(20) ⇕ a_4=- 10
5
a_5=-1/2a_(5-1) ⇕ a_5=-1/2a_4
a_5=-1/2(- 10) ⇕ a_5=5
6
a_6=-1/2a_(6-1) ⇕ a_6=-1/2a_5
a_6=-1/2(5) ⇕ a_6=- 5/2
Therefore, the first 6 terms of the sequence are 80, - 40, 20, - 10, 5, and - 52.
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.
