Question

write the set using the roster method.
$a = \left\\{ a \middle| 16 \leq a \leq 38 \text{ and } a \text{ is a multiple of } 3 \
ight\\}$

Explanation:

Step1: Find the first multiple of 3 ≥16

We start by finding the smallest multiple of 3 that is greater than or equal to 16. We know that \( 3\times 6 = 18\) (since \(3\times5 = 15<16\) and \(3\times6=18\geq16\)).

Step2: Find subsequent multiples of 3 within range

Then we keep adding 3 to 18 to get the next multiples of 3 and check if they are less than or equal to 38.

• \(18 + 3=21\)
• \(21+ 3 = 24\)
• \(24+ 3=27\)
• \(27 + 3=30\)
• \(30+ 3=33\)
• \(33+ 3=36\)
• \(36 + 3=39\) (but \(39>38\), so we stop here)

Answer:

\(A=\{18, 21, 24, 27, 30, 33, 36\}\)