What is the 38th term of 459,450,441,..

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]

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