The sum of first fifteen terms of an AP is 675 and the sum of next fifteen terms is 2025. Find the common difference of the AP.

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Solution

The correct option is A 6
Sum of first fifteen terms
$= S_{15} = (\frac{15}{2}) [2 a + 14 d] = 675$
$\Rightarrow 2 a + 14 d = 90 . . . . . . . (i)$

Sum of first 30 terms
$= S_{30} = (\frac{30}{2}) [2 a + 29 d] = 675 + 2025 = 2700$
$\Rightarrow 2 a + 29 d = 180 . . . . . . (i i)$

Subtracting (i) from (ii)

$15 d = 90 \Rightarrow d = 6.$

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