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Review: Consecutive Odd Integers
Explanation
The missing word here is "average." For a life of
simplified computations, when you hear the word "sum" you want to think
"average" (and vice versa). We can
use the cross-multiplied average formula:
Let's apply it to the fact that the sum of the first 4
integers is 656:
If this is the average of consecutive odd integers, then
the integers must be 161, 163, 165, and 167, which balance in pairs around 164.
Therefore, the last four numbers in the sequence must be 169, 171, 173, 175. We
could add these up to find the answer... or, we could use the average formula to
find their sum! They are balanced around 172, so that is their average, and
there are four of them, so
The correct answer is (A).
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