The average of the first 27 even natural numbers is:

For any arithmetic progression (AP), the average of all its terms equals the average of the first term and the last term: Average = (First term + Last term) ÷ 2. The first n even natural numbers form an AP with first term 2 and common difference 2, so the nth term equals 2 × n.

1. Identify the AP for this sequence: first term = 2, common difference = 2, and number of terms n = 27.

2. Find the last (27th) term using last term = first term + (n − 1) × common difference = 2 + (27 − 1) × 2 = 2 + 52 = 54.

3. Apply the AP average formula: Average = (First term + Last term) ÷ 2 = (2 + 54) ÷ 2 = 56 ÷ 2 = 28.

As an independent check, use the sum formula instead: Sum of n terms = (n ÷ 2) × (First term + Last term) = (27 ÷ 2) × 56 = 27 × 28 = 756. Dividing this sum by the number of terms gives Average = 756 ÷ 27 = 28, which matches the value obtained above.

So, the average of the first 27 even natural numbers is 28.