Solution

Given that the average of 35 consecutive even numbers is 44, we need to find the sum of the first and last numbers.

 

Let the first number be x and the last number be x+68 (since the difference between each consecutive even number is 2, and there are 34 steps between the first and last numbers).

 

The average of these numbers is given by:

\(Average = {\text{Sum of first and last numbers​} \over 2}\)

 

Given that the average is 44: 

\(44 = {x + x + 68 \over 2}\)

 

Simplifying:

\(44 = {2x + 68 \over 2}\)

 \(44 = x + 34\)

 

Solving for x:

x = 44 − 34 = 10

 

Thus, the first number is 10 and the last number is 10 + 68 = 78

 

The sum of the first and last numbers is:  10 + 78 = 88