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 3.
First Six Terms: 2, 6, 18, 54, 162, 486 Graph:
Practice makes perfect
We are asked to write the first 6 terms of a sequence, given a recursive rule.
a_1&=2
a_n&=3a_(n-1)
To do so, we will use a table.
n
a_n=3a_(n-1)
a_n
1
a_1=2
2
2
a_2=3a_(2-1) ⇕ a_2=3 a_1
a_2=3( 2) ⇕ a_2= 6
3
a_3=3a_(3-1) ⇕ a_3=3 a_2
a_3=3( 6) ⇕ a_3=18
4
a_4=3a_(4-1) ⇕ a_4=3a_3
a_4=3(18) ⇕ a_4=54
5
a_5=3a_(5-1) ⇕ a_5=3a_4
a_5=3(54) ⇕ a_5=162
6
a_6=3a_(6-1) ⇕ a_6=3a_5
a_6=3(162) ⇕ a_6=486
Therefore, the first 6 terms of the sequence are 2, 6, 18, 54, 162, and 486.
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.
