Question

The sum of the first n positive integers can be found using the formula n(n+1)/2. How many integers must be added to get 253 as the sum.

Answer 1

Answer:

22

Step-by-step explanation:

Using the given expression and the sum, we can set up an equation and solve for the value of 'n':

$\frac{n(n+1)}{2}=253$

Multiply both sides by '2':  

$2(\frac{n(n+1)}{2})=253(2)$

n(n+1) = 506

Distribute: n² + n - 506 = 0

Factor:  (n + 23) (n - 22) = 0

Set each equation equal to '0' and solve:

n + 23 = 0    n - 22 = 0

n = -23   or n = 22

Since the problem says the integers are positive, then n = 22.