Average

To find the average of all positive even integers less than or equal to 40, we first identify these numbers: 2, 4, 6, ..., 40.

This sequence is an arithmetic sequence where:

First term (a₁) = 2,

Last term (a_n) = 40,

Common difference (d) = 2.

To find the number of terms (n), use the formula for the n-th term of an arithmetic sequence: a_n = a₁ + (n-1)×d.
40 = 2 + (n-1)×2
40 - 2 = 2(n-1)
38 = 2(n-1)
19 = n-1
n = 20

The average of an arithmetic sequence can be calculated by the formula: Average = (a₁ + a_n) / 2.
Average = (2 + 40) / 2 = 42 / 2 = 21.

Thus, the average of all positive even integers less than or equal to 40 is 21