The image contains multiple arithmetic sequence problems in Indonesian. I'll provide solutions to a few questions from the image.

Problem 1:

Find the 15th term of the arithmetic sequence 70, 61, 52, ...

Given:

• First term $a = 70$
• Common difference $d = 61 - 70 = -9$

The $n$-th term formula for an arithmetic sequence is: $U_n = a + (n-1) \cdot d$ For the 15th term: $U_{15} = 70 + (15-1) \cdot (-9) = 70 + 14 \cdot (-9) = 70 - 126 = -56$ Answer: -56 (Option D)

Problem 2:

Find the 24th term of the arithmetic sequence 38, 35, 32, ...

Given:

• First term $a = 38$
• Common difference $d = 35 - 38 = -3$

For the 24th term: $U_{24} = 38 + (24-1) \cdot (-3) = 38 + 23 \cdot (-3) = 38 - 69 = -31$ Answer: -31 (Option C)

Problem 3:

If $2x, 4x+1, 14$ form an arithmetic sequence, find $x$.

The terms $2x, 4x+1, 14$ must satisfy the condition that the difference between consecutive terms is constant: $(4x+1) - 2x = 14 - (4x+1)$ Simplifying both sides: $2x + 1 = 14 - 4x - 1$ $2x + 1 = 13 - 4x$ Add $4x$ to both sides: $6x + 1 = 13$ Subtract 1 from both sides: $6x = 12$ $x = 2$ Answer: $x = 2$ (Option C)

Would you like more detailed explanations for any of these?

Here are 5 additional questions to expand your understanding:

1. What is the general formula for the sum of an arithmetic sequence?
2. How can we determine the common difference if we are given two terms from a sequence?
3. How does the formula for the $n$-th term of an arithmetic sequence change when the sequence is increasing?
4. What are the key differences between arithmetic and geometric sequences?
5. How can arithmetic sequences be applied in real-life situations?

Tip: Always double-check if the given sequence is arithmetic by ensuring the difference between consecutive terms is constant before applying formulas.