Choose the correct answer from the given four options:
The $ 11^{\text {th }} $ term of the AP: $ -5, \frac{-5}{2}, 0, \frac{5}{2}, \ldots $ is
(A) $ -20 $
(B) 20
(C) $ -30 $
(D) 30

Given: 

AP: \( -5, \frac{-5}{2}, 0, \frac{5}{2}, \ldots \)

To do: 

We have to find the \( 11^{\text {th }} \) term of the AP.

Solution:

Here,

$a_1 = -5, a_2=\frac{-5}{2}$

This implies,

$d=a_2-a_1$

$=\frac{-5}{2}-(-5)$

$=\frac{-5+10}{2}$

$=\frac{5}{2}$

Therefore,

$a_{11}=a+(11-1)d$

$=-5+10\times \frac{5}{2}$

$=-5+25$

$=20$

Therefore, the \( 11^{\text {th }} \) term of the AP is 20.