Answer:
The 30th term is 83
Step-by-step explanation:
we know that
An arithmetic sequence is a sequence of numbers such that the difference of any two successive members of the sequence is a constant called the common difference d
in this problem
[tex]a_1=-4\\a_2=-1\\a_3=2\\a_4=5\\a_5=8[/tex]
so
[tex]a_2-a_1=-1-(-4)=3\\a_3-a_2=-2-(-1)=3\\a_4-a_3=-5-2=3\\a_5-a_4=-8-5=3[/tex]
The common difference d is 3
We can write an Arithmetic Sequence as a rule:
[tex]a_n=a_1+d(n-1)[/tex]
Find out the 30th term
we have
[tex]n=30\\d=3\\a_1=-4[/tex]
substitute
[tex]a_n=-4+(3)(30-1)[/tex]
[tex]a_n=-4+(3)(29)[/tex]
[tex]a_n=83[/tex]
