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 six terms of a sequence, given its recursive rule.
a_1&=8
a_n&=1.5 a_(n-1), for n>1To 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 six 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.
