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Question

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A.\[4,6,8\]

B.\[6,8,10\]

C.\[8,10,12\]

D.\[10,12,14\]

Answer

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Let the first term of the series be a

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}} \\

\]

Hence ,

\[

{\text{a = 8}} \\

{\text{a + 2 = 10}} \\

{\text{a + 4 = 12}} \\

\]

Therefore the three consecutive even integers are 8,10,12.

So