MCQ
Choose the correct answer from the given four options : What is the common difference of an $AP$ in which $a_{18}- a_{14}= 32?$
- ✓$8$
- B$-8$
- C$-4$
- D$4$
✓
Answer
Correct option: A.
$8$
Given, $a_{18}- a_{14}= 32$
$[\therefore a_n= a + (n - 1)d]$
$\Rightarrow a + (18 - 1)d - [a + (14 - 1)d] = 32$
$\Rightarrow a + 17d - a - 13d = 32$
$\Rightarrow 4d = 32$
$\Rightarrow d = 8$
which is the required common difference of an $AP$.
$[\therefore a_n= a + (n - 1)d]$
$\Rightarrow a + (18 - 1)d - [a + (14 - 1)d] = 32$
$\Rightarrow a + 17d - a - 13d = 32$
$\Rightarrow 4d = 32$
$\Rightarrow d = 8$
which is the required common difference of an $AP$.
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