Answer:
[tex]a_3_8=364[/tex]
Step-by-step explanation:
we know that
In an Arithmetic Sequence the difference between one term and the next is a constant, and this constant is called the common difference
we have
[tex]31,40,49,58,...[/tex]
Let
[tex]a_1=31\\a_2=40\\a_3=49\\a_4=58[/tex]
we have that
[tex]a_2-a_1=40-31=9[/tex]
[tex]a_3-a_2=49-40=9[/tex]
[tex]a_4-a_3=58-49=9[/tex]
so
The common difference is equal to 9
We can write an Arithmetic Sequence as a rule:
[tex]a_n=a_1+d(n-1)[/tex]
where
a_n is the nth term
a_1 is the first term
d is the common difference
n is the number of terms
Find the 38th term of the arithmetic sequence
we have
[tex]a_1=31\\d=9\\n=38[/tex]
substitute the values
[tex]a_3_8=31+9(38-1)[/tex]
[tex]a_3_8=31+9(37)[/tex]
[tex]a_3_8=364[/tex]
