Question

I really need help with these..

Answer 1

OPTION C: 85

Explanation:

We are given the sequence
`$ \{a_n\} = \{-5, -(7)/(2), -2, -(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 = -(7)/(2) + 5 = (3)/(2) $`

Therefore,
`$ a_(61) = a + 60d $`

`$ \implies a_(61) = -5 + 60((3)/(2)) $`

`$ \implies a_(61) = - 5 + 90 = $` 85.

Hence, the answer.