what  is the sum of the first 15 terms of the arithmetic sequence where the first term is 7 and the common difference is 3?

To find the sum of the first 15 terms of an arithmetic sequence, we can use the formula for the sum of an arithmetic sequence:

\[
S_n = \frac{n}{2} \times (2a + (n - 1) \cdot d)
\]

Where:
- \(S_n\) is the sum of the first \(n\) terms.
- \(n\) is the number of terms (15 in this case).
- \(a\) is the first term (7 in this case).
- \(d\) is the common difference (3 in this case).

Now, let's plug in the values:

\[
S_{15} = \frac{15}{2} \times (2 \cdot 7 + (15 - 1) \cdot 3)
\]
\[
S_{15} = \frac{15}{2} \times (14 + 42)
\]
\[
S_{15} = \frac{15}{2} \times 56
\]
\[
S_{15} = \frac{15 \times 56}{2} = \frac{840}{2} = 420
\]

So, the sum of the first 15 terms of the sequence is **420**.

Would you like more details or have any questions?

Here are 5 related questions to expand on this concept:
1. How do you find the 10th term of an arithmetic sequence?
2. What happens to the sum if the common difference is negative?
3. Can you derive the formula for the sum of an arithmetic sequence?
4. How does the formula change for the sum of an infinite arithmetic sequence?
5. What is the sum of the first 20 terms of the same sequence?

**Tip:** In arithmetic sequences, the middle term (or average of the first and last terms) times the number of terms also gives the sum!

What is the sum of the first 15 terms of the arithmetic sequence where the first term is 7 and the common difference is 3?

Discover how to calculate the sum of the first 15 terms of an arithmetic sequence with a first term of 7 and a common difference of 3. This detailed solution explains the key concepts and formulas, suitable for students in Grades 9-10.

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