Answer:
[tex]a_6_3=371[/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]-1,5,11,...[/tex]
Let
[tex]a_1=-1\\a_2=5\\a_3=11[/tex]
[tex]a_2-a_1=5-(-1)=5+1=6[/tex]
[tex]a_3-a_2=11-5=6[/tex]
The common difference is [tex]d=6[/tex]
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
d is the common difference
a_1 is the first term
n is the number of terms
Find the 63rd term of the arithmetic sequence
we have
[tex]n=63\\d=6\\a_1=-1[/tex]
substitute
[tex]a_6_3=-1+6(63-1)[/tex]
[tex]a_6_3=-1+6(62)[/tex]
[tex]a_6_3=-1+372[/tex]
[tex]a_6_3=371[/tex]
