Answer:
The 65th term is
[tex]a_{65} = 35[/tex]
Step-by-step explanation:
We are given that the sequence provided is an arithmetic sequence. Even if this information were not provided we could deduce the same by noting that the difference between consecutive terms is constant
7/2 - 3 = 7/2 - 6/2 = 1/2
4 - 7/2 = 8/2 - 7/2 = 1/2
9/2 - 4 = 9/2 -8/2 = 1/2
A sequence of numbers where the difference between consecutive numbers is the same throughout the sequence is known as an arithmetic sequence
The constant difference, [tex]d[/tex], is known as the common difference
If we represent the first term in the sequence as [tex]a_1[/tex] then the formula for the nth term in the sequence,
[tex]a_n = a_1 + d(n - 1)[/tex]
In the given sequence
[tex]a_1=3[/tex]
[tex]d = 1/2[/tex]
[tex]n = 65[/tex] (65th term is what we want)
[tex]a_{65} = 3 + 1/2 * (65-1)\\\\a_{65} = 3 + 1/2 * 64\\\\a_{65} = 3 + 32\\\\a_{65} = 35\\\\[/tex]