The given formula means that after the first term of the sequence, every term a_(n+1) is the sum of the previous term a_n and 4.
- 3, 1, 5, 9, 13
Practice makes perfect
We are asked to write the first five terms of a sequence, given a recursive formula.
a_1&=- 3
a_(n+1)&=a_n+4
To do so, we will use a table. Notice that to find a_2 we will substitute n=1, to find a_3 we will substitute n=2, and so on.
n
a_(n+1)=a_n+4
a_n+4
a_(n+1)
-
a_1=- 3
-
- 3
1
a_(1+1)=a_1+4
a_1+4= - 3+4
1
2
a_(2+1)=a_2+4
a_2+4= 1+4
5
3
a_(3+1)=a_3+4
a_3+4= 5+4
9
4
a_(4+1)=a_4+4
a_4+4= 9+4
13
Therefore, the first five terms of the sequence are - 3, 1, 5, 9, and 13.
