The required terms are [tex]a_n=n-6[/tex] and [tex]a_{10}=4[/tex].
Given:
The given arithmetic sequence is:
[tex]-5,-4,-3,-2,..[/tex]
To find:
The [tex]nth[/tex] term and the [tex]10th[/tex] term of the given arithmetic sequence.
Explanation:
The [tex]nth[/tex] term of an arithmetic sequence is:
[tex]a_n=a+(n-1)d[/tex]
Where, [tex]a[/tex] is the first term and [tex]d[/tex] is the common difference.
In the given sequence the first term is [tex]-5[/tex] and the common difference is [tex]-4-(-5)=1[/tex].
Now, the [tex]nth[/tex] term of the given arithmetic sequence is:
[tex]a_n=-5+(n-1)(1)[/tex]
[tex]a_n=-5+n-1[/tex]
[tex]a_n=n-6[/tex]
Substituting [tex]n=10[/tex], we get
[tex]a_{10}=10-6[/tex]
[tex]a_{10}=4[/tex]
Therefore, the required terms are [tex]a_n=n-6[/tex] and [tex]a_{10}=4[/tex].
Learn more:
https://brainly.com/question/20343207
