Read the story and respond to the requests below.

Question

Henry generates 5 emails to raise money for a fundraiser. He sends the email to 5 people for the fundraiser. If each of the five recipients sends the email to five more people, 25 emails are generated. If each of the twenty-five recipients sends five emails, 125 emails are generated.

Write the sequence represented by the story.
Is the sequence arithmetic or geometric?
Does it have a common difference or common ratio?
What is the common difference or common ratio?
What are the next three terms?

Answer 1

The sequence represented by the story can be described as follows:

• The first term is 5 emails (sent by Henry).
• The second term is 25 emails (5 recipients each sending the email to 5 more people).
• The third term is 125 emails (25 recipients each sending the email to 5 more people).

Now, let's analyze the sequence:

1. Sequence: The terms generated are 5, 25, and 125.

2. Type of Sequence: This sequence is geometric because each term is found by multiplying the previous term by a constant.

3. Common Ratio: The common ratio can be calculated as follows:

   • From 5 to 25: \( \frac{25}{5} = 5 \)
   • From 25 to 125: \( \frac{125}{25} = 5 \)

   Thus, the common ratio is 5.

4. Next Three Terms: To find the next three terms in the sequence, we multiply the last known term (125) by the common ratio (5):

   • Fourth term: \( 125 \times 5 = 625 \)
   • Fifth term: \( 625 \times 5 = 3125 \)
   • Sixth term: \( 3125 \times 5 = 15625 \)

Therefore, the next three terms in the sequence are 625, 3125, and 15625.

To summarize:

• Sequence: 5, 25, 125, 625, 3125, 15625
• Type: Geometric
• Common ratio: 5
• Next three terms: 625, 3125, 15625