Question

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

Answer 1

The 38th term of 459,450,441,.. will be:

`a_(13)=351`

Explanation:

Given the sequence

`459,450,441,..`

An arithmetic sequence has a constant difference 'd' and is defined by

`a_n=a_1+\left(n-1\right)d`

computing the differences of all the adjacent terms

`450-459=-9,\:\quad \:441-450=-9`

so

`d=-9`

The first element of the sequence is

`a_1=459`

so the nth term will be

`a_n=-9\left(n-1\right)+459`

`a_n=-9n+468`

Putting n=38 to find the 38th term

`a_n=-9n+468`

`a_(13)=-9\left(13\right)+468`

`a_(13)=-117+468`

`a_(13)=351`

Therefore, the 38th term of 459,450,441,.. will be:

`a_(13)=351`