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The average of 7 consecutive numbers is 20. What is the largest of these numbers?
22
23
24
25
23
For any set of an odd number of consecutive numbers, the average is always the exact middle number. Since there are 7 numbers, the 4th number is 20, and the largest (7th) number is 20+3=23.
Number of consecutive numbers = 7, Average of the 7 numbers = 20
Average=Number┬аof┬аtermsSum┬аof┬аnumbersтАЛ
For any set of an odd number of consecutive numbers, the average is always the exact middle number. Since there are 7 numbers, the 4th number is 20, and the largest (7th) number is 20+3=23.
Students often assume the first number is the average or try to set up an algebraic equation starting from x and solving a lengthy linear equation, wasting precious exam time.
Identify the Middle Number
Since the numbers are consecutive and there are 7 of them (an odd quantity), the average of the set represents the exact middle (4th) term in the sequence.
x4тАЛ=20
Determine the Position of the Largest Number
The largest number in a set of 7 consecutive numbers is the 7th number, which is 3 positions ahead of the 4th number.
Largest┬аnumber=x4тАЛ+3
Calculate the Value
Substitute the middle term into the expression to find the largest number: 20+3=23.
20+3=23
B is correct because the average of 7 consecutive numbers is the 4th number (20), making the largest number 20+3=23.
This property applies to any arithmetic progression with an odd number of terms, where the median equals the mean.
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