Problems based on Numbers Test 1

Sum of 15 different natural numbers = 13 × 15 = 195
Derive the maximum value of second largest natural number among a group of 15 natural numbers.
First thirteen natural numbers must be the smallest possible.
So, the first thirteen natural numbers will be 1, 2, 3 ….. 13
Sum of first thirteen natural numbers $=\frac{\mathit{n}\left(\mathit{n}+1\right)}{2}=\frac{13\left(13+1\right)}{2}=91$
So, the sum of the fourteenth and the fifteenth natural numbers = 195 - 91 = 104
The two numbers 51, 53.
So, the second largest number 51.