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 14.
Terms: 32, 8, 2, 12, 18, and 132 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&=32
a_n&=1/4a_(n-1), for n>1To do so, we will use a table.
n
a_n=1/4a_(n-1)
1/4a_(n-1)
a_n
1
a_1=32
-
32
2
a_2=1/4a_(2-1)
1/4( a_1)=1/4( 32)
8
3
a_3=1/4a_(3-1)
1/4( a_2)=1/4( 8)
2
4
a_4=1/4a_(4-1)
1/4(a_3)=1/4(2)
1/2
5
a_5=1/4a_(5-1)
1/4(a_4)=1/4(1/2)
1/8
6
a_6=1/4a_(6-1)
1/4(a_5)=1/4(1/8)
1/32
Therefore, the first 6 terms of the sequence are 32, 8, 2, 12, 18, and 132.
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.
