Write the first five term of the arithmetic with the first term , a1=7, and the common difference , d=-5

To find the first five terms of an arithmetic sequence, you can use the formula:

\[
a_n = a_1 + (n-1) \times d
\]

Given:
- \( a_1 = 7 \)
- \( d = -5 \)

Now, let's calculate the first five terms:

1. **First term** (\(a_1\)):  
   \[
   a_1 = 7
   \]

2. **Second term** (\(a_2\)):  
   \[
   a_2 = 7 + (2-1) \times (-5) = 7 - 5 = 2
   \]

3. **Third term** (\(a_3\)):  
   \[
   a_3 = 7 + (3-1) \times (-5) = 7 - 10 = -3
   \]

4. **Fourth term** (\(a_4\)):  
   \[
   a_4 = 7 + (4-1) \times (-5) = 7 - 15 = -8
   \]

5. **Fifth term** (\(a_5\)):  
   \[
   a_5 = 7 + (5-1) \times (-5) = 7 - 20 = -13
   \]

So, the first five terms of the arithmetic sequence are:

\[
\mathbf{7}, \mathbf{2}, \mathbf{-3}, \mathbf{-8}, \mathbf{-13}
\]

Would you like more details or have any questions? Here are some related questions:

1. How do you find the sum of the first 10 terms of this sequence?
2. What is the 10th term of this sequence?
3. Can you derive the general formula for the \( n \)-th term of this sequence?
4. What happens if the common difference was positive?
5. How would you calculate the sum of the first 5 terms?

**Tip:** In an arithmetic sequence with a negative common difference, each term decreases by the same amount as you move forward in the sequence.

Learn how to calculate the first five terms of an arithmetic sequence with the first term a1=7 and the common difference d=-5. This problem involves using the arithmetic sequence formula to find each term step-by-step. Suitable for Grades 7-9.

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