https://file.aiquickdraw.com/mathbot/file/1727410124509b59deywk.jpg

The image contains four summation problems in a sequence. Here's a transcription of each summation expression for clarity:

7. \( \sum_{k=1}^{4} 3k \)  
8. \( \sum_{k=2}^{9} (2k + 3) \)  
9. \( \sum_{i=2}^{6} (-1)^i \)  
10. \( \sum_{n=3}^{7} (2 - n) \)  

Let's solve each of these summations one by one:

### 1. Problem 7:
\[
\sum_{k=1}^{4} 3k = 3(1) + 3(2) + 3(3) + 3(4) = 3 + 6 + 9 + 12 = 30
\]

### 2. Problem 8:
\[
\sum_{k=2}^{9} (2k + 3) = (2(2) + 3) + (2(3) + 3) + \dots + (2(9) + 3)
\]
This evaluates to:
\[
(4 + 3) + (6 + 3) + (8 + 3) + (10 + 3) + (12 + 3) + (14 + 3) + (16 + 3) + (18 + 3) = 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 = 112
\]

### 3. Problem 9:
\[
\sum_{i=2}^{6} (-1)^i = (-1)^2 + (-1)^3 + (-1)^4 + (-1)^5 + (-1)^6 = 1 - 1 + 1 - 1 + 1 = 1
\]

### 4. Problem 10:
\[
\sum_{n=3}^{7} (2 - n) = (2 - 3) + (2 - 4) + (2 - 5) + (2 - 6) + (2 - 7) = -1 - 2 - 3 - 4 - 5 = -15
\]

### Final Answers:
- Problem 7: \( 30 \)
- Problem 8: \( 112 \)
- Problem 9: \( 1 \)
- Problem 10: \( -15 \)

Would you like further details or have any questions?

Here are some related questions to deepen your understanding:
1. What is the general formula for summing an arithmetic sequence?
2. How do alternating sums like \( (-1)^i \) behave as \( i \) increases?
3. How can you apply summation properties to simplify large sums?
4. What patterns emerge in sums of linear functions like \( 2k + 3 \)?
5. How does shifting summation indices affect the result?

**Tip**: When dealing with summations, breaking down each term before adding can help simplify the process, especially when facing complex expressions.

Hitunglah Jumlah-Jumlah Berikut: 
7. ∑ (3k) from k=1 to 4
8. ∑ (2k + 3) from k=2 to 9
9. ∑ (-1)^i from i=2 to 6
10. ∑ (2 - n) from n=3 to 7

Explore detailed solutions for summation problems involving arithmetic sequences, alternating sums, and algebraic expressions. This guide includes step-by-step calculations suitable for Grades 8-10, covering concepts like arithmetic sequence formulas and summation notation.

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