Question 2

Let's find the common property of the given numbers and then list the next three numbers.

Step 1 — Identify the pattern

We are given the numbers 11, 13, 17, 19. Let's check if these numbers are prime. A prime number has only two factors: 1 and itself.

$\text{Factors of } 11: 1, 11$ $\text{Factors of } 13: 1, 13$ $\text{Factors of } 17: 1, 17$ $\text{Factors of } 19: 1, 19$

$\boxed{\text{All the given numbers are prime numbers.}}$

Step 2 — Find the next three numbers

We need to find the next three prime numbers after 19. Let's list numbers starting from 20 and check if they are prime.

$20 \text{ is not prime (divisible by } 2, 4, 5, 10).$ $21 \text{ is not prime (divisible by } 3, 7).$ $22 \text{ is not prime (divisible by } 2, 11).$ $23 \text{ is prime (divisible only by } 1, 23).$ $24 \text{ is not prime.}$ $25 \text{ is not prime.}$ $26 \text{ is not prime.}$ $27 \text{ is not prime.}$ $28 \text{ is not prime.}$ $29 \text{ is prime (divisible only by } 1, 29).$ $30 \text{ is not prime.}$ $31 \text{ is prime (divisible only by } 1, 31).$

$\boxed{\text{The next three prime numbers are } 23, 29, 31.}$

Answer

(i) The numbers 11, 13, 17, 19 are all prime numbers. (ii) The next three numbers that fit this pattern are 23, 29, 31.