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The question from the image is:

**"The mean of a set of 'n' consecutive multiples of 5 is 'p'. How many more consecutive multiples of 5 following 'n' should be included in the earlier set to increase the mean by 25?"**

Let’s break this down step by step:

1. The consecutive multiples of 5 can be represented as: 
   \( 5, 10, 15, \dots, 5n \). These are the first \( n \) multiples of 5.

2. The mean \( p \) of these numbers is:
   \[
   p = \frac{5 + 10 + 15 + \dots + 5n}{n}
   \]
   This simplifies to:
   \[
   p = \frac{5(1 + 2 + 3 + \dots + n)}{n} = \frac{5 \times \frac{n(n+1)}{2}}{n} = \frac{5(n+1)}{2}
   \]

3. Now, we are tasked with adding additional multiples of 5 to the set and increasing the mean by 25. Let’s assume we add \( x \) more consecutive multiples, so the new set contains \( n + x \) elements.

   The new mean will be:
   \[
   p_{\text{new}} = p + 25 = \frac{\text{sum of the new set}}{n + x}
   \]

4. The sum of the new set will be the sum of the original set plus the next \( x \) multiples of 5, which are \( 5(n+1), 5(n+2), \dots, 5(n+x) \).

   The sum of these additional terms is:
   \[
   5[(n+1) + (n+2) + \dots + (n+x)] = 5\left( \frac{x(2n+x+1)}{2} \right)
   \]

5. Now we set up the equation:
   \[
   \frac{5(n+1)}{2} + 25 = \frac{\frac{5n(n+1)}{2} + 5\left( \frac{x(2n+x+1)}{2} \right)}{n + x}
   \]
   Simplifying and solving for \( x \), we find that \( x = 9 \).

Thus, **9 more consecutive multiples of 5** should be added to the set to increase the mean by 25.

Would you like further details or clarification? 

Here are some related questions:
1. How do you calculate the sum of an arithmetic series?
2. What is the relationship between the mean and the sum of a set of numbers?
3. How does adding new terms affect the mean of a set?
4. How do you solve equations involving summations?
5. What are consecutive multiples and how are they formed?

**Tip:** When increasing the mean of a set by adding numbers, consider both the number and magnitude of the values being added!

The mean of a set of 'n' consecutive multiples of 5 is 'p'. How many more consecutive multiples of 5 following 'n' should be included in the earlier set to increase the mean by 25?

Learn how to determine how many more consecutive multiples of 5 are needed to increase the mean of a set by 25. This problem involves concepts like arithmetic series, mean, and algebra, suitable for Grades 9-12.

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