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Calculate the values of $x$ and $y$
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$x=4$ and $y=26$

Explanation:

Since the pattern is $2;x;12;y$ then

the first differences are as follows:

$x-2; 12-x; y-12$

Given that the second difference of the quadratic sequence is 6, then

$(12-x)-(x-2)=6$

and

$(y-12)-(12-x)$

Solving the first equation:

$12-x-x+2=6$

$14-2x=6$

$14-6=2x$

$\therefore x=4$

Solving the second equation:

$(y-12)-(12-x)=6$

$y-12-12+x=6$

$y-24+4=6$ remember $x=4$

$y=6+24-4$

$\therefore y=26$

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