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The average of seven consecutive odd numbers is 41. What is the smallest of these numbers?
37
33
39
35
35
For consecutive sequences with an odd number of terms, the average is always the exact middle term. Simply subtract 2 for each step backward from the middle term to reach the smallest number.
There are 7 consecutive odd numbers with an average of 41.
Average=nSumтАЛ=MiddleTerm(for┬аodd┬аnumber┬аof┬аconsecutive┬аterms)
For consecutive sequences with an odd number of terms, the average is always the exact middle term. Simply subtract 2 for each step backward from the middle term to reach the smallest number.
Students often try to set up an algebraic equation like x+(x+2)+(x+4)+тЛп=41├Ч7, which is time-consuming and prone to calculation errors.
Identify the middle term
Since there are 7 (an odd number) consecutive odd numbers, their average is equal to the median (middle term).
Middle┬аTerm=41
Sequence positioning
With 7 numbers, the 4th term is the middle term. To find the 1st term (smallest), we need to go back 3 positions.
1stTerm=4thTermтИТ3├Ч2=41тИТ6
Calculate the smallest number
Subtracting 6 from the middle term of 41 gives the smallest odd number in the sequence.
41тИТ6=35
D is correct because 35 is the first number in the sequence 35, 37, 39, 41, 43, 45, 47, which averages to 41.
This property of the median also applies to any Arithmetic Progression where the number of terms is odd, which is a powerful shortcut in Data Interpretation and Statistics questions.
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