Write the first five terms of the arithmetic sequence whose first term is 4​, and whose common difference is 7.
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To write the first five terms of the arithmetic sequence, we use the formula for the \( n \)-th term of an arithmetic sequence:

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

Where:
- \( a_1 \) is the first term,
- \( d \) is the common difference,
- \( n \) is the term number.

### Given:
- \( a_1 = 4 \)
- \( d = 7 \)

#### Calculate the first five terms:

1. For \( n = 1 \):
   \[
   a_1 = 4
   \]

2. For \( n = 2 \):
   \[
   a_2 = a_1 + (2-1)d = 4 + 7 = 11
   \]

3. For \( n = 3 \):
   \[
   a_3 = a_1 + (3-1)d = 4 + 2 \cdot 7 = 18
   \]

4. For \( n = 4 \):
   \[
   a_4 = a_1 + (4-1)d = 4 + 3 \cdot 7 = 25
   \]

5. For \( n = 5 \):
   \[
   a_5 = a_1 + (5-1)d = 4 + 4 \cdot 7 = 32
   \]

### First Five Terms:
\[
4, 11, 18, 25, 32
\]

Would you like further explanations or examples on arithmetic sequences?

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### Related Questions:
1. How do you find the common difference of an arithmetic sequence from two terms?
2. What is the formula for the sum of the first \( n \) terms of an arithmetic sequence?
3. How do arithmetic sequences differ from geometric sequences?
4. What are the applications of arithmetic sequences in real-world scenarios?
5. How can you determine if a given sequence is arithmetic?

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**Tip:** To check if a sequence is arithmetic, calculate the difference between consecutive terms. If it's constant, the sequence is arithmetic!

Write the first five terms of the arithmetic sequence whose first term is 4, and whose common difference is 7.

Learn how to calculate the first five terms of an arithmetic sequence with a first term of 4 and a common difference of 7. This problem uses the formula a_n = a_1 + (n-1)d to find the sequence terms step by step. Suitable for students in Grades 6-8.

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