Write the pseudocode to print all multiples of 5 between 10 and 25 (including both 10 and 25).

Exercise · Q3

Q. Write the pseudocode to print all multiples of 5 between 10 and 25 (including both 10 and 25).

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Concept understanding — Iteration With Condition

Iteration With Condition

Imagine you're searching for a lost key in a dark room. You don't know how many steps you'll need — you just keep moving your hand along the floor until you feel the metal. You're repeating the same action (searching), but you stop only when a specific condition is met (you touch the key).

That's iteration with a condition. It's the idea of repeating a process not a fixed number of times, but while something remains true, or until something becomes true.

The Intuition

Most everyday loops are conditional. You don't say "I will stir the tea exactly 47 times." You say "I will stir the tea until the sugar dissolves." The number of stirs depends on when the condition (sugar dissolved) is satisfied.

In programming and mathematics, this is far more natural than a fixed-count loop. You often don't know in advance how many repetitions you'll need — you only know the rule that should keep you going, or the rule that should stop you.

The Precise Statement

An iteration with condition is a control structure that repeatedly executes a block of statements as long as a given Boolean condition evaluates to true. The condition is checked before (or after) each execution of the block.

The two standard forms are:

1. While loop (entry-controlled)

while (condition):
    statement(s)

The condition is tested first. If it's true, the block runs; then the condition is tested again. If it's false from the start, the block never runs.

2. Do-while loop (exit-controlled)

do:
    statement(s)
while (condition)

The block runs once unconditionally, then the condition is tested. If true, it repeats; if false, it stops. This guarantees at least one execution.

Watch out

A common mistake is writing a condition that never becomes false — an infinite loop. For example, while (x > 0) where x is never decreased. The program will run forever (or crash). Always ensure the body of the loop changes something that affects the condition.

A Concrete Example

Suppose you want to find the smallest power of 2 greater than 1000. You don't know the answer in advance — you need to keep doubling until you cross the threshold.

n = 1
while (n <= 1000):
    n = n * 2

Trace it:

Start: n = 1. Is 1 <= 1000? Yes → n = 2
n = 2. Is 2 <= 1000? Yes → n = 4
... continues ...
n = 512. Is 512 <= 1000? Yes → n = 1024
n = 1024. Is 1024 <= 1000? No → stop

The loop ran 10 times. The final value of n is 1024, which is the smallest power of 2 greater than 1000.

Tip

When designing a conditional loop, ask yourself: What must change each iteration so that the condition eventually becomes false? If nothing changes, you have an infinite loop. If the change moves the condition in the wrong direction, you also have an infinite loop.

Why This Matters

Iteration with condition is the backbone of algorithms that search, approximate, or process data of unknown size. You use it when:

Reading a file until you hit the end
Asking a user for input until they give a valid answer
Computing a square root by repeated approximation until the error is small enough
Traversing a linked list until you find a null pointer

It's not just a programming construct — it's a way of thinking: repeat until done, where "done" is defined by a condition, not a count.

Start at 10 and step through the numbers to 25, printing the multiples of 5:

SET num = 10
WHILE num <= 25
    PRINT num
    num = num + 5
END WHILE

(Stepping by 5 from 10 visits exactly the multiples.) Output produced:

✓Final answer

The pseudocode prints 10, 15, 20, 25 — all multiples of 5 from 10 to 25 inclusive.

Loop from 10 to 25 and print the multiples of 5 — either step by 5 directly, or test each number with MOD; the output is 10, 15, 20, 25.

The idea (iteration with a condition). Printing a regular sequence is the natural job of a loop. Two equally valid designs: (a) step by 5 starting at a multiple, so every visited number is automatically a multiple; or (b) scan every number from 10 to 25 and use the remainder operator (MOD) to test divisibility. Version (a) is more efficient; version (b) shows the test explicitly.

Pseudocode — version (a), stepping by 5

PRINT_MULTIPLES_OF_5
    SET num = 10
    WHILE num <= 25
        PRINT num
        num = num + 5
    END WHILE
END

Pseudocode — version (b), testing with MOD

PRINT_MULTIPLES_OF_5
    SET num = 10
    WHILE num <= 25
        IF num MOD 5 == 0 THEN
            PRINT num
        END IF
        num = num + 1
    END WHILE
END

Python verification

for num in range(10, 26, 5):
    print(num)

Expected output

Dry run of version (a)

Iteration	num at test	num <= 25?	Printed
1	10	yes	10
2	15	yes	15
3	20	yes	20
4	25	yes	25
5	30	no — loop ends	—

Watch out

"Including both 10 and 25" means the condition must be num <= 25 (and range(10, 26, 5) in Python — range(10, 25, 5) would wrongly stop at 20).

✓Final answer

The loop prints 10, 15, 20, 25 — every multiple of 5 between 10 and 25, both ends included.

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Q.Write the pseudocode to print all multiples of 5 between 10 and 25 (including both 10 and 25).

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