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!