Let's solve the problems shown in the image:

Problem 25:

Arrange the numbers and symbols of the following and choose the correct answer: $1, 2, 3, +, -$

We need to find an arrangement of these numbers and symbols that forms a valid equation.

Possible solution:
$1 + 2 = 3$ This means $1 + 2 = 3$ is the correct equation.

So, the answer is 3.

Problem 26:

Arrange the numbers and symbols of the following and choose the correct answer: $2, 3, 4, +, -$

Possible solution: $4 - 2 = 2$ or $3 + 2 = 5$ Since neither of these results match any of the choices, let's try different combinations.

$4 - 3 = 1$ The possible answer is 1.

Problem 27:

What is the next number in the sequence: 3, 6, 10, 15,...?

Looking at the sequence:

• The difference between consecutive terms is increasing by 1 each time:
  • $6 - 3 = 3$
  • $10 - 6 = 4$
  • $15 - 10 = 5$

So, the next difference should be $6$.

• $15 + 6 = 21$

The answer is 21.

Would you like more details on any of these problems or explanations on other similar problems?

Follow-up Questions:

1. Can you find another valid equation for the set $1, 2, 3, +, -$ besides $1 + 2 = 3$?
2. What are other possible equations for the set $2, 3, 4, +, -$ that might not be in the given options?
3. How can you derive the formula for the sequence in Problem 27?
4. Can you identify a sequence where the difference between terms decreases instead of increasing?
5. How would the pattern change if the increment between sequence terms was by a different constant number?

Tip:

When identifying patterns in sequences, try to find a consistent difference or ratio between consecutive terms first.