The given rule means that, after the first term of the sequence, every term a_n is the product of the previous term a_(n-1) and 1.5.
First Six Terms: 8, 12, 18, 27, 40.5, and 60.75 Graph:
Practice makes perfect
We are asked to write the first 6 terms of a sequence, given its recursive rule.
a_1&=8
a_n&=1.5 a_(n-1), for n>1
To do so, we will use a table.
n
a_n=1.5a_(n-1)
1.5 a_(n-1)
a_n
1
a_1=8
-
8
2
a_2=1.5 a_(2-1)
1.5 a_1=1.5 (8)
12
3
a_3=1.5 a_(3-1)
1.5 a_2 = 1.5 ( 12)
18
4
a_4=1.5 a_(4-1)
1.5 a_3=1.5 (18)
27
5
a_5=1.5 a_(5-1)
1.5 a_4=1.5 (27)
40.5
6
a_6=1.5 a_(6-1)
1.5 a_5 = 1.5 (40.5)
60.75
The first 6 terms of the sequence are 8, 12, 18, 27, 40.5, and 60.75.
To graph them, 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.
