Answer to Question #119082 in Algorithms for Raahim Agha

Question

Draw a flow diagram for an algorithm which calculates how many numbers 1, 2, 3…n have to be added to reach a total greater thah 500. Output the answer n.

 

Answer 1

First, write the equation for the sum of the arithmetic progression with difference d=1 and the first element a₁=1:

$$S=\frac{n[2a_1+(n-1)d]}{2}=\frac{n^2+n}{2}.$$

The sum must be greater than 500:

$$\frac{n^2+n}{2}>500,$$

transform the inequality:

$$n^2+n-1000>0.$$

Algorithm:

for int n=1 to infinity:  

if n^2+n-1000<0,

then continue

else print(n)

Draw the flow diagram: