The given rule means that after the first term of the sequence, every term a_n is the previous term a_(n-1) multiplied by 10.
First Six Terms of the Sequence: 0.7, 7, 70, 700, 7000, 70 000 Graph:
Practice makes perfect
We are asked to write the first 6 terms of a sequence, given a recursive rule.
a_1&=0
a_n&=10a_(n-1)To do so, we will use a table.
n
a_n=10a_(n-1)
10a_(n-1)
a_n
1
a_1=0.7
-
0.7
2
a_2=10a_(2-1)
10 a_1=10* 0.7
7
3
a_3=10a_(3-1)
10 a_2=10* 7
70
4
a_4=10a_(4-1)
10 a_3=10* 70
700
5
a_5=10a_(5-1)
10 a_4=10* 700
7000
6
a_6=10a_(6-1)
10 a_5=10* 7000
70 000
Therefore, the first 6 terms of the sequence are 0.7, 7, 70, 700, 7000, and 70 000. To graph the 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.
