Let’s solve the problems from the uploaded image one by one. Here's the detailed solution:

1. Diket baris aritmatika 2, 6, 10, 14, ...

• Formula for an arithmetic sequence:
  $U_n = a + (n - 1) \cdot b$ where:

  • $a$ = first term,
  • $b$ = difference,
  • $n$ = term number.

• Here:

  • $a = 2$,
  • $b = 6 - 2 = 4$.

Suku ke-15 ($U_{15}$): $U_{15} = 2 + (15 - 1) \cdot 4 = 2 + 56 = 58$ Answer: $U_{15} = 58$.

2. Diket baris aritmatika 3, 7, 11, 15, ...

• Formula:
  $U_n = a + (n - 1) \cdot b$

• Here:

  • $a = 3$,
  • $b = 7 - 3 = 4$.

Suku ke-15 ($U_{15}$): $U_{15} = 3 + (15 - 1) \cdot 4 = 3 + 56 = 59$ Answer: $U_{15} = 59$.

3. Diket $U_1 = 1$ dan $U_5 = 13$

• Formula for $U_n$: $U_n = a + (n - 1) \cdot b$

• Here:

  • $U_1 = a = 1$,
  • $U_5 = 13$.

From $U_5$: $13 = 1 + (5 - 1) \cdot b$ $13 = 1 + 4b \implies 4b = 12 \implies b = 3$

(a) Nilai beda ($b$):

$b = 3$.

(b) Suku pertama ($a$):

$a = 1$.

(c) Suku ke-9 ($U_9$):

$U_9 = 1 + (9 - 1) \cdot 3 = 1 + 24 = 25$ Answer:
(a) $b = 3$,
(b) $a = 1$,
(c) $U_9 = 25$.

Do you want more details or have any questions?

Related Questions:

1. What is the general formula for the nth term of an arithmetic sequence?
2. How do you find the sum of the first $n$ terms of an arithmetic sequence?
3. Can the difference $b$ be negative in an arithmetic sequence? Explain with an example.
4. How do you derive the formula for the nth term of an arithmetic sequence?
5. What are real-life applications of arithmetic sequences?

Tip: Always identify $a$ (first term) and $b$ (difference) before solving arithmetic sequence problems.