The question asks to identify which of the given sequences are arithmetic sequences (barisan aritmetika). An arithmetic sequence is one where the difference between consecutive terms is constant. Let's analyze each option:

Analyzing the sequences:

1. (a) 15, 18, 21, 24, ...

   • Differences: $18 - 15 = 3$, $21 - 18 = 3$, $24 - 21 = 3$
   • Constant difference = 3. This is an arithmetic sequence.

2. (b) 8, -2, -12, -22, ...

   • Differences: $-2 - 8 = -10$, $-12 - (-2) = -10$, $-22 - (-12) = -10$
   • Constant difference = -10. This is an arithmetic sequence.

3. (c) 5, -10, 20, -40, ...

   • Differences: $-10 - 5 = -15$, $20 - (-10) = 30$, $-40 - 20 = -60$
   • The differences are not constant. Not an arithmetic sequence.

4. (d) 48, 24, 12, 6, ...

   • Differences: $24 - 48 = -24$, $12 - 24 = -12$, $6 - 12 = -6$
   • The differences are not constant. Not an arithmetic sequence.

5. (e) -½, 3, -12, 48, ...

   • Differences: $3 - (-½) = 3.5$, $-12 - 3 = -15$, $48 - (-12) = 60$
   • The differences are not constant. Not an arithmetic sequence.

6. (f) √5, $1 + √5$, $2 + √5$, $3 + √5$, ...

   • Differences: $(1 + √5) - √5 = 1$, $(2 + √5) - (1 + √5) = 1$, $(3 + √5) - (2 + √5) = 1$
   • Constant difference = 1. This is an arithmetic sequence.

7. (g) $\frac{1}{2}, \frac{1}{3}, \frac{1}{4}, \frac{1}{5}, ...$

   • Differences: $\frac{1}{3} - \frac{1}{2} = -\frac{1}{6}$, $\frac{1}{4} - \frac{1}{3} = -\frac{1}{12}$
   • The differences are not constant. Not an arithmetic sequence.

8. (h) $\frac{3}{16}, \frac{3}{8}, \frac{3}{4}, \frac{3}{2}, ...$

   • Convert to the same denominator: $\frac{3}{16}, \frac{6}{16}, \frac{12}{16}, \frac{24}{16}$
   • Differences: $\frac{6}{16} - \frac{3}{16} = \frac{3}{16}$, $\frac{12}{16} - \frac{6}{16} = \frac{6}{16}$
   • The differences are not constant. Not an arithmetic sequence.

9. (i) $a, ab, ab^2, ab^3, ...$

   • This appears to be a geometric sequence, not arithmetic. Not an arithmetic sequence.

10. (j) $a, a + k^2, a + 2k^2, a + 3k^2, ...$

    • Differences: $(a + k^2) - a = k^2$, $(a + 2k^2) - (a + k^2) = k^2$
    • Constant difference = $k^2$. This is an arithmetic sequence.

Conclusion:

The arithmetic sequences are:

• (a) 15, 18, 21, 24, ...
• (b) 8, -2, -12, -22, ...
• (f) √5, $1 + √5$, $2 + √5$, $3 + √5$, ...
• (j) $a, a + k^2, a + 2k^2, a + 3k^2, ...$

Would you like a detailed explanation for any specific sequence or have any other questions?

Related Questions:

1. What is the general formula for an arithmetic sequence?
2. How can you determine the nth term of an arithmetic sequence?
3. What is the sum formula for the first n terms of an arithmetic sequence?
4. Can a geometric sequence also be arithmetic? If so, under what condition?
5. How do you identify a sequence if it is neither arithmetic nor geometric?

Tip:

To quickly check if a sequence is arithmetic, calculate the differences between consecutive terms. If they are all the same, it's an arithmetic sequence.