The arithmetic average of seven consecutive odd number must be the fourth number which, by definition, is odd.
If the average is not the arithmetic average, then the question is ambiguous.
In either case the question has no valid answer.
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Consecutive numbers are whole numbers whose difference is 1.
8 10 12 14 16
The smallest of seven consecutive even integers whose sum is 700 is 94.
Any pair of consecutive numbers will have an odd total. 10 and 12 are consecutive even numbers that total 22.
There is no set of 3 consecutive odd numbers whose product is 6,873. However, there is a set of 3 consecutive odd numbers whose sum is 6,873: 2289, 2291, and 2293.