Final answer:
To find the largest number in a group of three consecutive even integers, solve the equation x + (x+2) + (x+4) = 618, where x is the smallest even integer. The largest number in the group is x+4.
Step-by-step explanation:
To solve this problem, let's assume the smallest even integer as 'x'. The next two consecutive even integers will be 'x+2' and 'x+4'. According to the problem, the sum of three consecutive even integers is 618. So, we can write the equation as x + (x+2) + (x+4) = 618. Solving this equation, we get the value of 'x' as 204. Therefore, the largest number in the group is x+4, which is 208.
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