Basic sequence examples with detailed solutions for Algebra 2

📚 Quick Study Guide

• 🔢 Arithmetic Sequence: A sequence where the difference between consecutive terms is constant. The formula is $a_n = a_1 + (n-1)d$, where $a_n$ is the nth term, $a_1$ is the first term, $n$ is the term number, and $d$ is the common difference.
• 📈 Geometric Sequence: A sequence where each term is multiplied by a constant to get the next term. The formula is $a_n = a_1 * r^(n-1)$, where $a_n$ is the nth term, $a_1$ is the first term, $n$ is the term number, and $r$ is the common ratio.
• ➕ Sum of an Arithmetic Series: The sum of the first n terms of an arithmetic sequence. The formula is $S_n = \frac{n}{2}(a_1 + a_n)$, where $S_n$ is the sum of the first n terms, $n$ is the number of terms, $a_1$ is the first term, and $a_n$ is the nth term.
• ✖️ Sum of a Geometric Series: The sum of the first n terms of a geometric sequence. The formula is $S_n = \frac{a_1(1 - r^n)}{1 - r}$, where $S_n$ is the sum of the first n terms, $a_1$ is the first term, $r$ is the common ratio, and $n$ is the number of terms.
• ♾️ Infinite Geometric Series: If $|r| < 1$, the sum of an infinite geometric series is $S = \frac{a_1}{1 - r}$, where $a_1$ is the first term and $r$ is the common ratio.

🧪 Practice Quiz

1. Question 1: What is the 10th term of the arithmetic sequence 2, 5, 8, 11, ...?
1. A) 29
2. B) 32
3. C) 35
4. D) 38
2. Question 2: What is the 7th term of the geometric sequence 3, 6, 12, 24, ...?
1. A) 96
2. B) 192
3. C) 384
4. D) 768
3. Question 3: Find the sum of the first 6 terms of the arithmetic sequence 1, 4, 7, 10, ...
1. A) 45
2. B) 51
3. C) 57
4. D) 63
4. Question 4: Find the sum of the first 5 terms of the geometric sequence 2, 6, 18, 54, ...
1. A) 242
2. B) 244
3. C) 246
4. D) 248
5. Question 5: What is the common difference of the arithmetic sequence where $a_1 = 5$ and $a_{20} = 43$ ?
1. A) 1.8
2. B) 2.0
3. C) 2.2
4. D) 2.4
6. Question 6: What is the common ratio of the geometric sequence where $a_1 = 4$ and $a_4 = 32$?
1. A) 1
2. B) 2
3. C) 3
4. D) 4
7. Question 7: Find the sum of the infinite geometric series 9 + 3 + 1 + 1/3 + ...
1. A) 13.5
2. B) 14.0
3. C) 14.5
4. D) 15.0