Question

I really need help with these..

Answer 1

Answer:

OPTION C: 85

Step-by-step explanation:

We are given the sequence $\{a_n\} = \{-5, -\frac{7}{2}, -2, -\frac{1}{2}, 1, \hdots\}$.

The general form of an Arithmetic Progression (AP) is given by:

$\{a, a + d, a + 2d, a + 3d, \hdots, a + nd, \hdots\}$

where, $'a'$ is the first term of the sequence and

$'d'$ is the common difference.

Here, $a$ = -5

$d = a + d - a = -\frac{7}{2} + 5 = \frac{3}{2}$

Therefore, $a_{61} = a + 60d$

$\implies a_{61} = -5 + 60(\frac{3}{2})$

$\implies a_{61} = - 5 + 90 =$ 85.

Hence, the answer.