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What are three consecutive even integers such that the sum of the smallest and twice the second is more than the third?

Answer 1

Kennedy Adams

This is true for all three positive consecutive even integers.

Let the three consecutive even integers be #2n#, #2n+2# and #2n+4#.

As the sum of the smallest i.e. #2n# and twice the second i.e. #2(2n+2)# is more than the third i.e. #2n+4#, we have

#2n+2(2n+2)>2n+4#

i.e. #2n+4n+4>2n+4#

i.e. #4n>0# or #n>0#

Thus, the claim that the third is greater than the sum of the smallest and twice the second,

holds true for each of the three consecutive positive even numbers.

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Answer from HIX Tutor

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