1. The problem is to find the sum of integers from 1 to $n$ using the given flowchart algorithm. 2. The algorithm initializes $\text{sum} = 0$ and $a = 1$. 3. It then adds $a$ to $\text{sum}$, so $\text{sum} = \text{sum} + a$. 4. It checks if $a = n$. If not, it increments $a$ by 1 and repeats the addition. 5. When $a = n$, it prints the sum and ends. 6. This is equivalent to calculating the sum of the first $n$ natural numbers. 7. The formula for the sum of the first $n$ natural numbers is: $$\text{sum} = \frac{n(n+1)}{2}$$ 8. This formula is derived by pairing numbers from the start and end of the sequence: $$1 + n = n + 1$$ $$2 + (n-1) = n + 1$$ and so on, with $\frac{n}{2}$ such pairs. 9. Therefore, the final answer after the flowchart completes is: $$\boxed{\frac{n(n+1)}{2}}$$ This sum represents the total of all integers from 1 up to $n$.