Find the common difference of an AP

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Solution

The correct option is A 2
Let $a$ be the first term and $d$ be their common difference of the AP.
Then, $n t h$ term of the AP $a_{n} = a + (n - 1) d$
Given, $a_{3} = 6$
$=> a + (3 - 1) d = 6$
$=> a + 2 d = 6$ -- (1)
Also, $a_{1} 7 = 34$
$=> a + (17 - 1) d = 34$
$=> a + 16 d = 34$ -- (2)
Subtracting eqn 2 from eqn 1, we get
$14 d = 28$
$=> d = 2$

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