The given rule means that, after the first term of the sequence, every term a_n is the sum of the previous term a_(n-1) and 2.5.
First Six Terms of the Sequence: - 7.5, - 5, - 2.5, 0, 2.5, 5 Graph:
Practice makes perfect
We are asked to write the first 6 terms of a sequence, given a recursive rule.
a_1&=- 7.5
a_n&=a_(n-1)+2.5
To do so, we will use a table.
n
a_n=a_(n-1)+2.5
a_(n-1)+2.5
a_n
1
a_1=- 7.5
-
- 7.5
2
a_2=a_(2-1)+2.5
a_1+2.5= - 7.5+2.5
- 5
3
a_3=a_(3-1)+2.5
a_2+2.5= - 5+2.5
- 2.5
4
a_4=a_(4-1)+2.5
a_3+2.5=- 2.5+2.5
5
a_5=a_(5-1)+2.5
a_4+2.5= +2.5
2.5
6
a_6=a_(6-1)+2.5
a_5+2.5=2.5+2.5
5
Therefore, the first 6 terms of the sequence are - 7.5, - 5, - 2.5, 0, 2.5, and 5.
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.
