What is an arithmetic sequence? Definition and examples

📚 Quick Study Guide

• 🔢 An arithmetic sequence is a sequence of numbers such that the difference between any two consecutive terms is constant. This constant difference is called the common difference.
• ➕ To find the next term in an arithmetic sequence, simply add the common difference to the previous term.
• 📈 The general formula for the nth term ($a_n$) of an arithmetic sequence is: $a_n = a_1 + (n-1)d$, where $a_1$ is the first term, $n$ is the term number, and $d$ is the common difference.
• 🧮 The sum ($S_n$) of the first n terms of an arithmetic sequence is: $S_n = \frac{n}{2}(a_1 + a_n)$ or $S_n = \frac{n}{2}[2a_1 + (n-1)d]$.
• 💡 Key terms: Sequence, Term, Common Difference, First Term.

Practice Quiz

1. What is the common difference in the arithmetic sequence: 2, 5, 8, 11, ...?
   1. 1
   2. 2
   3. 3
   4. 4
2. What is the 10th term of the arithmetic sequence with a first term of 3 and a common difference of 2?
   1. 19
   2. 20
   3. 21
   4. 22
3. Which of the following sequences is an arithmetic sequence?
   1. 1, 4, 9, 16, ...
   2. 2, 4, 8, 16, ...
   3. 1, 5, 9, 13, ...
   4. 1, 3, 6, 10, ...
4. What is the sum of the first 5 terms of the arithmetic sequence: 1, 3, 5, 7, ...?
   1. 15
   2. 20
   3. 25
   4. 30
5. If the 3rd term of an arithmetic sequence is 7 and the common difference is 2, what is the first term?
   1. 1
   2. 2
   3. 3
   4. 4
6. What is the formula for finding the nth term of an arithmetic sequence?
   1. $a_n = a_1 + nd$
   2. $a_n = a_1 - (n-1)d$
   3. $a_n = a_1 + (n-1)d$
   4. $a_n = a_1 - nd$
7. The first term of an arithmetic sequence is -1, and the common difference is 3. Find the 7th term.
   1. 14
   2. 17
   3. 20
   4. 23