The first five terms of the sequence are 1, 4, 7, 10, 13.
Solution:
Given data:
[tex]a_{1}=1[/tex]
[tex]a_{n}=a_{n-1}+3[/tex]
General term of the arithmetic sequence.
[tex]a_{n}=a_{n-1}+d[/tex], where d is the common difference.
d = 3
[tex]a_{n}=a_{n-1}+3[/tex]
Put n = 2 in [tex]a_{n}=a_{n-1}+3[/tex], we get
[tex]a_{2}=a_1+3[/tex]
[tex]a_{2}=1+3[/tex]
[tex]a_2=4[/tex]
Put n = 3 in [tex]a_{n}=a_{n-1}+3[/tex], we get
[tex]a_{3}=a_2+3[/tex]
[tex]a_{3}=4+3[/tex]
[tex]a_3=7[/tex]
Put n = 4 in [tex]a_{n}=a_{n-1}+3[/tex], we get
[tex]a_{4}=a_3+3[/tex]
[tex]a_{4}=7+3[/tex]
[tex]a_4=10[/tex]
Put n = 5 in [tex]a_{n}=a_{n-1}+3[/tex], we get
[tex]a_{5}=a_4+3[/tex]
[tex]a_{5}=10+3[/tex]
[tex]a_5=13[/tex]
The first five terms of the sequence are 1, 4, 7, 10, 13.
