Let's examine the sequence:
$10, 22, 34, 46, 58$

Step 1: Calculate the differences between consecutive terms:

• $22 - 10 = 12$
• $34 - 22 = 12$
• $46 - 34 = 12$
• $58 - 46 = 12$

Step 2: Identify the pattern

The common difference between each pair of numbers is $12$. This indicates that the sequence follows an arithmetic progression with a difference of $12$.

Step 3: Find the next number

To find the next number, we add $12$ to the last term in the sequence: $58 + 12 = 70$

Thus, the next number in the sequence is 70.

---

Would you like further details or have any other questions?

Here are 5 related questions to expand on this:

1. What is an arithmetic progression, and how is it defined?
2. How would you find the general formula for the $n$-th term of this sequence?
3. Could this sequence have a quadratic or geometric pattern as well?
4. What is the sum of the first $n$ terms in this arithmetic progression?
5. How do you differentiate between arithmetic and geometric sequences?

Tip: Always verify patterns by checking multiple consecutive terms for consistency!