Find the average of squares of consecutive even numbers from 1 to 20?

Given:

The average of squares of consecutive even numbers from 1 to 20

Formula Used:

\(Avg = \frac{sum\ of \ square\ of \ consecutive \ even \ number}{total \ number}\)

The average of squares of consecutive even numbers from 1 to 20 we will follow the following steps:

As we know,

Even numbers from 1 to 20 are 2,4,6,8,10,12,14,16,18

Now,

Square of even number =

2²= 4, 4²= 16, 6²= 36, 8² = 64, 10² = 100, 12² = 144 , 14² = 196, 16² = 256,

18² = 324 , 20² = 400

Now,

Sum of squares of consecutive even numbers

⇒ 4 + 16 + 36 + 64 + 100 + 144 + 196 + 256 + 324 +400 = 1540

The average Sum of squares of consecutive even numbers is

⇒ 1540 / 10 = 154