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 - 4.
First Six Terms: - 7, 28, - 112, 448, - 1792, 7168 Graph:
Practice makes perfect
We are asked to write the first six terms of a sequence, given a recursive rule.
a_1&=- 7
a_n&=- 4a_(n-1)To do so, we will use a table.
n
a_n=- 4a_(n-1)
a_n
1
a_1=- 7
- 7
2
a_2=- 4a_(2-1) ⇕ a_2=- 4 a_1
a_2=- 4*( - 7) ⇕ a_2= 28
3
a_3=- 4a_(3-1) ⇕ a_3=- 4 a_2
a_3=- 4* 28 ⇕ a_3= - 112
4
a_4=- 4a_(4-1) ⇕ a_4=- 4 a_3
a_4=- 4*( - 112) ⇕ a_4= 448
5
a_5=- 4a_(5-1) ⇕ a_5=- 4 a_4
a_5=- 4* 448 ⇕ a_5= - 1792
6
a_6=- 4a_(6-1) ⇕ a_6=- 4 a_5
a_6=- 4*( - 1792) ⇕ a_6=7168
Therefore, the first 6 terms of the sequence are - 7, 28, - 112, 448, - 1792, and 7168. 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.
