The average of thirteen consecutive integers is 36. If two times the smallest of these 13 integers is added to the largest of these 13 integers what will be the sum obtained?

Correct option is C

Given:-

The average of thirteen consecutive integers is 36.

Formula Used:-

The average of nnn consecutive integers can be expressed as

​$$\text{Average} = \frac{\text{Sum of all integers}}{n}$$​​
Solution:-

Let the smallest integer be x.

Since the average of 13 consecutive integers is 36, the sum; 

​$$13 \times 36 = 468$$ 

Now, the 13 consecutive integers is:

​$$x, x+1, x+2, \dots, x+12$$​​

The sum of these integers is:

​$$x + (x+1) + (x+2) + \dots + (x+12) = 13x + 78$$​​

As, we know the sum is 468, so:

​$$13x + 78 = 468 \\13x = 390 \\x = 30$$​​

Therefore, the smallest integer is 30, and the largest integer is $$30 + 12 = 42$$​​

Now,  $$2 \cdot \text{smallest} + \text{largest}$$;

​$$2 \times 30 + 42 = 60 + 42 = 102$$​​

So, the sum obtained is 102