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The equation shown is \( a_n = 4n - 5 \) for \( 1 \leq n \leq 5 \). This defines a sequence where \( a_n \) is the term corresponding to each value of \( n \) within the given range (from 1 to 5).

Let's calculate the values of \( a_n \) for each \( n \) from 1 to 5:

1. For \( n = 1 \):  
   \( a_1 = 4(1) - 5 = 4 - 5 = -1 \)

2. For \( n = 2 \):  
   \( a_2 = 4(2) - 5 = 8 - 5 = 3 \)

3. For \( n = 3 \):  
   \( a_3 = 4(3) - 5 = 12 - 5 = 7 \)

4. For \( n = 4 \):  
   \( a_4 = 4(4) - 5 = 16 - 5 = 11 \)

5. For \( n = 5 \):  
   \( a_5 = 4(5) - 5 = 20 - 5 = 15 \)

Thus, the sequence is:  
\( -1, 3, 7, 11, 15 \).

Would you like further details or clarification?

### Related Questions:
1. What is the general form of an arithmetic sequence?
2. How can you derive the sum of this sequence?
3. How would the sequence change if the formula were modified to \( a_n = 4n + 5 \)?
4. What is the difference between arithmetic and geometric sequences?
5. Can you graph this sequence?

### Tip:
In arithmetic sequences, the common difference between consecutive terms can be found by subtracting one term from the next!

Given the formula a_n = 4n - 5 for 1 ≤ n ≤ 5, find the sequence.

Explore how to find the sequence for the formula a_n = 4n - 5 with a step-by-step solution for each value of n from 1 to 5. Suitable for Grades 6-8, this problem covers arithmetic progression and sequence generation.

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