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The average of 7 consecutive numbers is 33. The greatest of these numbers is:
30
28
36
33
36
For n consecutive numbers, the average is the middle number. To find the largest, add (nтИТ1)/2 to the average: 33+(7тИТ1)/2=33+3=36.
There are 7 consecutive numbers with an average of 33.
Greater=Average+2nтИТ1тАЛ
For n consecutive numbers, the average is the middle number. To find the largest, add (nтИТ1)/2 to the average: 33+(7тИТ1)/2=33+3=36.
Confusing the number of terms (n=7) with the number of additions needed; the greatest number is 3 steps away from the middle average, not 7.
Identify the property of consecutive numbers
For an odd number of consecutive terms, the average is always equal to the middle (median) term.
Middle=33
Position the sequence
Since there are 7 terms, the middle term is the 4th term. The sequence is 3 terms before and 3 terms after the middle term.
n=7,offset=27тИТ1тАЛ=3
Calculate the greatest number
The greatest number is 3 steps greater than the middle number.
33+3=36
C is correct because the average of 7 consecutive numbers is the 4th term, so the 7th (greatest) term is 33+3=36.
This property applies to any Arithmetic Progression where the number of terms is odd; for an even number of terms, the average falls exactly between the two middle terms.
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