The sum of five consecutive even numbers is equal to 260. what is the sum of the largest number amongst them and the half the square of the smallest numbers amongst them?

Sure, let's solve this step by step:

Step 1: Find the average of the five consecutive even numbers. Since they are consecutive and even, the average will be the middle number. So, 260/5 = 52.

Step 2: Identify the five consecutive even numbers. Since 52 is the middle number, the five numbers are 48, 50, 52, 54, and 56.

Step 3: Identify the smallest and largest numbers. The smallest number is 48 and the largest number is 56.

Step 4: Calculate half the square of the smallest number. (48^2)/2 = 1152.

Step 5: Add the largest number to half the square of the smallest number. 1152 + 56 = 1208.

So, the sum of the largest number amongst them and half the square of the smallest number amongst them is 1208.