As given by the question
There are given that the sequence:
[tex]64.5,\text{ 65, 65.5, 66, 66.5,}\ldots[/tex]
Now,
From the formula of the nth term of the arithmetic sequence:
[tex]a_n=a_1+(n-1)d[/tex]
Where,
[tex]\begin{gathered} a_1=65, \\ d=a_2-a_1 \\ d=65.5_{}-65 \\ d=0.5 \end{gathered}[/tex]
Then,
Put all the terms into the above formula:
So,
[tex]A=0.5n\ldots\text{.}(1)[/tex]
Now,
If the first term is 65
Then,
[tex]65-0.5=64.5[/tex]
Then,
Add the above value into equation (1)
So,
[tex]A=0.5n+64.5[/tex]
Hence, the correct option is C.
