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If the average of 5 consecutive odd numbers is 25, what is the largest number in the set?
27
29
31
25
29
Given: Average of 5 consecutive odd numbers = 25 ┬╖ Number of terms n = 5.
Average of 5 consecutive odd numbers = 25 ┬╖ Number of terms n = 5.
Average=NumberoftermsSumoftermsтАЛ
For consecutive numbers (or odd/even series), the average is always the middle term ┬╖ Since there are 5 numbers, the middle (3rd) term is 25; the next two odd numbers are 27 and 29.
Students often assume the average is the first number or try to form a long quadratic equation x+(x+2)+..., which is time-consuming and prone to calculation errors.
Identify the middle term
Since the sequence consists of an odd number of consecutive odd terms, the average is exactly the middle value.
MiddleTerm=25
Define the sequence
With the 3rd term being 25, the consecutive odd terms are: (3rd term - 4), (3rd term - 2), 3rd term, (3rd term + 2), (3rd term + 4).
$21, 23, 25, 27, 29$
Determine the largest term
The largest term is the 5th term in the sequence, which is calculated as 25 + 4.
Largest=29
B is correct because the sequence is 21, 23, 25, 27, 29, making the largest number 29.
This concept of the middle term being the average also applies to any Arithmetic Progression with an odd number of terms, a useful shortcut for Data Interpretation questions.