Answer:
The 38th term of 459,450,441,.. will be:
[tex]a_{13}=351[/tex]
Step-by-step explanation:
Given the sequence
[tex]459,450,441,..[/tex]
An arithmetic sequence has a constant difference 'd' and is defined by
[tex]a_n=a_1+\left(n-1\right)d[/tex]
computing the differences of all the adjacent terms
[tex]450-459=-9,\:\quad \:441-450=-9[/tex]
so
[tex]d=-9[/tex]
The first element of the sequence is
[tex]a_1=459[/tex]
so the nth term will be
[tex]a_n=-9\left(n-1\right)+459[/tex]
[tex]a_n=-9n+468[/tex]
Putting n=38 to find the 38th term
[tex]a_n=-9n+468[/tex]
[tex]a_{13}=-9\left(13\right)+468[/tex]
[tex]a_{13}=-117+468[/tex]
[tex]a_{13}=351[/tex]
Therefore, the 38th term of 459,450,441,.. will be:
[tex]a_{13}=351[/tex]
