Question

Find the three consecutive even integers such that the sum of the first two integers is the same as the sum of a third integer and $6$A.$4,6,8$B.$6,8,10$C.$8,10,12$D.$10,12,14$

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Hint: Here we can see that the integers are consecutive even integers and so the difference among them is of $2$. So, let the first number be a, and on the above-given basis, we form all the three terms and put it into the given condition and solve to get the required answer.

And so the second term will be ${\text{a + 2}}$
And third term will be ${\text{a + 4}}$
Now, put it into the equation given as the sum of the first two integers is the same as the sum of the third integer and $6$
${\text{a + (a + 2) = a + 4 + 6}} \\ \Rightarrow {\text{2a + 2 = a + 10}} \\ \Rightarrow {\text{a = 8}} \\$
${\text{a = 8}} \\ {\text{a + 2 = 10}} \\ {\text{a + 4 = 12}} \\$