Answer:
[tex]a_6_4=-313[/tex]
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
In this problem we have
2,-3,-8,...
Let
[tex]a_1=2\\a_2=-3\\a_3=-8[/tex]
[tex]a_2-a_1=-3-(2)=-5\\a_3-a_2=-8-(-3)=-5[/tex]
The common difference d is equal to -5
We can write an Arithmetic Sequence as a rule
[tex]a_n=a_1+d(n-1)[/tex]
where
d is the common difference
a_1 is the first term
n is the number or terms
Find the 64th term
we have
[tex]a_1=2[/tex]
[tex]d=-5[/tex]
[tex]n=64[/tex]
substitute
[tex]a_6_4=2+(-5)(64-1)[/tex]
[tex]a_6_4=-313[/tex]
