What is the common difference of an AP in which $a_{21} - a_{7} = 84 ?$

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Solution

Let a is the first term and d is the common difference of an AP

$a_{21} = a + (21 - 1) d = a + 20 d$

$a_{7} = a + (7 - 1) d = a + 6 d$

$a_{21} - 97 = 84$

$a + 20 d - a - 6 d = 84$

$14 d = 84$

$d = 6$

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