Answer:
OPTION C: 85
Step-by-step explanation:
We are given the sequence [tex]$ \{a_n\} = \{-5, -\frac{7}{2}, -2, -\frac{1}{2}, 1, \hdots\}[/tex].
The general form of an Arithmetic Progression (AP) is given by:
[tex]$ \{a, a + d, a + 2d, a + 3d, \hdots, a + nd, \hdots\} $[/tex]
where, [tex]$ 'a' $[/tex] is the first term of the sequence and
[tex]$ 'd' $[/tex] is the common difference.
Here, [tex]$ a $[/tex] = -5
[tex]$ d = a + d - a = -\frac{7}{2} + 5 = \frac{3}{2} $[/tex]
Therefore, [tex]$ a_{61} = a + 60d $[/tex]
[tex]$ \implies a_{61} = -5 + 60(\frac{3}{2}) $[/tex]
[tex]$ \implies a_{61} = - 5 + 90 = $[/tex] 85.
Hence, the answer.
