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1. Mengapa barisan bilangan ganjil yang terdiri dari 200 suku dengan bilangan 3, 5, 7, 9, ... 2n-1, 2n+1 ... merupakan suatu barisan aritmatika?

   • (A) karena beda antar sukunya tetap
   • (B) karena selisih antar sukunya tetap
   • (C) karena rasionya tetap
   • (D) karena ada pola yang beraturan

   Answer: (B) karena selisih antar sukunya tetap
   Explanation: The sequence of odd numbers (3, 5, 7, 9, ...) is an arithmetic sequence because the difference between consecutive terms (the common difference) is constant, which is 2.

2. Diketahui suku ke-5 dan suku ke-10 dari suatu deret aritmetika berturut-turut adalah 14 dan 29. Jika suku pertama deret tersebut 2, tentukan rumus suku ke-n deret tersebut!

   • (A) Un = 3n - 1
   • (B) Un = 5n - 4
   • (C) Un = 2n + 4
   • (D) Un = 4n - 6

   Answer: (B) Un = 5n - 4
   Explanation: Given the sequence information, the first term (a) is 2, and the common difference (d) can be found using the formula for the nth term: $U_n = a + (n-1) \times d$. Solving with the given terms, the formula is $U_n = 5n - 4$.

3. Dari suatu deret aritmetika diketahui suku pertama adalah 3 dan suku terakhir adalah 36. Jumlah semua suku deret tersebut adalah 208. Banyaknya suku pada deret tersebut adalah ...

   • (A) 13
   • (B) 12
   • (C) 15
   • (D) 14

   Answer: (B) 13
   Explanation: Use the sum formula $S_n = \frac{n}{2} \times (a + l)$ where $S_n = 208$, $a = 3$, and $l = 36$. Solving gives $n = 13$.

4. Dari 4 bilangan yang berurutan yang jumlah dari dua bilangan pertamanya sama dengan jumlah dua bilangan terakhir, maka jumlah bilangan yang paling besar adalah ...

   • (A) 10
   • (B) 14
   • (C) 20
   • (D) 15

   Answer: (B) 14
   Explanation: The numbers are in an arithmetic sequence. Let the first number be $x$. The numbers can be written as $x$, $x+1$, $x+2$, and $x+3$. If the sum of the first two equals the sum of the last two, solve the equation $2x + 1 = 2x + 5$ to find that the numbers are 3, 4, 5, 6, and the largest is 14.

5. Dua buah bilangan membentuk suatu barisan aritmetika dengan beda antar sukunya adalah 3. Jika suku tengahnya adalah 13, maka jumlah dua suku tersebut adalah ...

   • (A) 20
   • (B) 26
   • (C) 40
   • (D) 34

   Answer: (B) 26
   Explanation: In an arithmetic sequence with two terms, the middle term is the average of the two terms. So, the sum of the terms is twice the middle term: $13 \times 2 = 26$.

If you have any questions or would like further details on any of these solutions, feel free to ask!

Relative Questions:

1. How do you derive the common difference in an arithmetic sequence when given two terms?
2. Can the common ratio in a geometric sequence be negative? If so, what does that imply about the sequence?
3. How do you find the sum of an infinite geometric series?
4. How does one determine the number of terms in an arithmetic series when given the sum and first term?
5. What is the difference between an arithmetic sequence and an arithmetic series?

Tip: When dealing with sequences, always check the pattern by comparing differences (for arithmetic) or ratios (for geometric) between consecutive terms to ensure consistency.