What is the common difference of an AP in which a_ 27 - a_7 = 84? - Vidyadip

Question

What is the common difference of an AP in which $a_{27} - a_7 = 84?$

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Answer

Let 'a' is the first term and d is the common difference of the AP
Given:
$a_{27} - a_7 = 84$
$a_n= a + (n - 1)d$
$a_{27}= a + (27 - 1)d$
$a_7= a + (7 - 1)d$
$a_{27 -} a_7= 84$
$a + 26d - (a + 6d) = 84$
$a + 26d - a - 6d = 84$
$a - a + 26d - 6d = 84$
$26d - 6d = 84$
$20d = 84$
$\text{d} = \frac{84}{20} = \frac{21}{5}$
d = 4.2

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