The arithmetic mean of 3, 7, 11, ..., 51 is ______.
27
The series 3, 7, 11, ..., 51 is an arithmetic progression with common difference 4.
Number of terms: \(51 = 3+(n-1)\times4 \Rightarrow n-1=12 \Rightarrow n=13\).
For an AP, the arithmetic mean equals half the sum of the first and last terms: \(\dfrac{3+51}{2}=27\).
Hence, the arithmetic mean of the series is 27.
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