ITPEC FE Subject A April 2024 Question 6

Flowchart: Sum of First N Odd Numbers — find the loop exit condition for summing 1 + 3 + 5 + ... + (2N-1).

The algorithm uses counter i starting at 1, incrementing by 2 each iteration, accumulating into x.

• •Last value to add: 2N - 1
• •After adding it: i becomes 2N - 1 + 2 = 2N + 1
• •Exit when: i ≥ 2N + 1

Trace for N = 3 (expect 1 + 3 + 5 = 9):
- i=1 → x=1, i=3
- i=3 → x=4, i=5
- i=5 → x=9, i=7
- i=7 ≥ 7 → exit with x = 9 ✓

Why not others:
- (a) i ≥ 2N − 1 — exits before adding the last odd number
- (c) x ≥ 2N − 1 — compares the sum, not the counter
- (d) x ≥ 2N + 1 — compares the sum, not the counter

Key rule: In counter-based loops, the exit condition depends on the counter variable, not the accumulated result.

AI-generated — may contain errors