Choose the correct answer from the given four options:
What is the common difference of an AP in which $ a_{18}-a_{14}=32 $ ?
(A) 8
(B) $ -8 $
(C) $ -4 $
(D) 4
Given:
\( a_{18}-a_{14}=32 \)
To do:
We have to find the common difference of the AP.
Solution:
Let the common difference be $d$
Let $a$ be the first term of the A.P.
$\therefore a_{18}=a+( 18-1)d$
$\Rightarrow a_{18}=a+17d$
Similarly, $a_{14}=a+( 14-1)d$
$\Rightarrow a_{14}=a+13d$
$\therefore a_{18}-a_{14}=a+17d-a-13d=32$
$4d=32$
$d=\frac{32}{4}$
$d=8$
The common difference of the given AP is $8$.
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