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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Important Questions from Arithmetic Progression
If the nth term of a sequence is \(\frac{2 n+5}{7}\), then what is the sum of its first 140 terms?
What is the arithmetic mean of first 8 multiples of 13?
The average of five consecutive odd natural numbers is 27. The product of the first and fifth number is:
Find the sum of all the numbers between 100 to 200 which are divisible by 12.
In a garden, there are 6 daisy plants the first year. Each year, a gardener adds 3 new daisy plants the first year and loses 2 each year. He has 26 jasmine plants the first year and loses 2 each year. When will the number of daisy plants equal the number of jasmine plants after the first year?
