The sum of 2 consecutive even integers is at most 400. What are the numbers?

Answer 1

The largest pair of consecutive integers are 198 and 200.

If the sum of two equal even numbers is 400, the numbers will be 200+200. Therefore the largest possible consecutive even numbers which have a sum of 400 or less are 198 and 200 which have a sum of 398.

Any pair of consecutive numbers less than these will have a sum of less than 400.

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Answer 2

Genesis Allen

Let ( n ) be the smaller even integer. Then, the next consecutive even integer is ( n + 2 ). Their sum is ( n + (n + 2) = 2n + 2 ). We want this sum to be at most 400, so:

[ 2n + 2 \leq 400 ] [ 2n \leq 398 ] [ n \leq 199 ]

So, the smaller even integer can be at most 199. The larger even integer would be ( n + 2 ), which is at most ( 199 + 2 = 201 ). Therefore, the possible even integers are from 2 to 201.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.