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 5.
1, 6, 11, 16, 21
Practice makes perfect
We are asked to write the first five terms of a sequence, given a recursive formula.
a_1&=1
a_(n+1)&=a_n+5
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+5
a_n+5
a_(n+1)
-
a_1=1
-
1
1
a_(1+1)=a_1+5
a_1+5= 1+5
6
2
a_(2+1)=a_2+5
a_2+5= 6+5
11
3
a_(3+1)=a_3+5
a_3+5=11+5
16
4
a_(4+1)=a_4+5
a_4+5=16+5
21
Therefore, the first five terms of the sequence are 1, 6, 11, 16, and 21.
