The given rule means that, after the first term of the sequence, every term a_n is the half of the previous term a_(n-1).
First Six Terms of the Sequence: - 36, - 18, - 9, - 92, - 94, - 98 Graph:
Practice makes perfect
We are asked to write the first 6 terms of a sequence, given a recursive rule.
a_1&=- 36
a_n&= 12a_(n-1)
To do so, we will use a table.
n
a_n=1/2a_(n-1)
1/2a_(n-1)
a_n
1
a_1=- 36
-
- 36
2
a_2=1/2a_(2-1)
1/2 a_1=1/2( - 36)
- 18
3
a_3=1/2a_(3-1)
1/2 a_2=1/2( - 18)
- 9
4
a_4=1/2a_(4-1)
1/2a_3=1/2(- 9)
- 9/2
5
a_5=1/2a_(5-1)
1/2a_4=1/2(- 9/2)
- 9/4
6
a_6=1/2a_(6-1)
1/2a_5=1/2(- 9/4)
- 9/8
Therefore, the first 6 terms of the sequence are - 36, - 18, - 9, - 92, - 94, and - 98.
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.
