Given:
The arithmetic sequence is
[tex]\dfrac{1}{2},1,1\dfrac{1}{2},2[/tex]
To find:
The nth term of the given arithmetic sequence and then find [tex]a_{10}[/tex].
Solution:
We have,
[tex]\dfrac{1}{2},1,1\dfrac{1}{2},2[/tex]
Here,
First term: [tex]a=\dfrac{1}{2}[/tex]
Common difference: [tex]d=1-\dfrac{1}{2}=\dfrac{1}{2}[/tex]
nth term of an arithmetic sequence is
[tex]a_n=a+(n-1)d[/tex]
where, a is first term and d is common difference.
[tex]a_n=\dfrac{1}{2}+(n-1)\dfrac{1}{2}[/tex]
[tex]a_n=\dfrac{1}{2}+\dfrac{1}{2}n-\dfrac{1}{2}[/tex]
[tex]a_n=\dfrac{1}{2}n[/tex]
Now, put n=10, to find [tex]a_{10}[/tex].
[tex]a_{10}=\dfrac{1}{2}(10)[/tex]
[tex]a_{10}=5[/tex]
Therefore, the nth term of the given arithmetic sequence is [tex]a_n=\dfrac{1}{2}n[/tex] and the value of [tex]a_{10}[/tex] is 5.
