The value of n is____.

Question

The sum of the first n natural numbers, S= 1+2+3+...+ n, is given by                S= 1/2n(n+1). If the sum of the first n natural numbers is 55, determine the value of n.

Answer 1

Using the formula S = n(n+1)/2, we have

 

55 = n(n+1)/2

110 = n(n+1)

110 = n² + n

0 = n² + n - 110

0 = (n - 10)(n + 11)

n = 10, -11

 

Since n is a natural number, n = -11 is not a solution, so n = 10 is the solution.