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.
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