Question:
Choose the correct answer in each of the following questions:
What is the common difference of an AP in which $a_{18}-a_{14}=32 ?$
(a) 8
(b) $-8$
(c) 4
(d) $-4$
Solution:
Let a be the first term and d be the common difference of the AP. Then,
$a_{18}-a_{14}=32$
$\Rightarrow(a+17 d)-(a+13 d)=32 \quad\left[a_{n}=a+(n-1) d\right]$
$\Rightarrow 4 d=32$
$\Rightarrow d=8$
Thus, the common difference of the AP is 8.
Hence, the correct answer is option is A.
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