Arithmetic Sequences

An arithmetic sequence is a sequence of numbers in which the difference between any two consecutive terms is constant. This difference is called the common difference.

The general form of an arithmetic sequence is:

a, a + d, a + 2d, a + 3d, ...

Where:

• a is the first term of the sequence
• d is the common difference between the terms

Finding the nth Term of an Arithmetic Sequence

The formula to find the nth term of an arithmetic sequence is:

a_n = a + (n - 1)d

Where:

• a_n is the nth term of the sequence
• a is the first term of the sequence
• d is the common difference
• n is the term number

Finding the Sum of the First n Terms of an Arithmetic Sequence

The formula to find the sum of the first n terms of an arithmetic sequence is:

S_n = (n/2)(a + l)

Where:

• S_n is the sum of the first n terms
• n is the number of terms
• a is the first term
• l is the last term

Study Guide

1. What is an arithmetic sequence?
2. What is the formula to find the nth term of an arithmetic sequence?
3. What is the formula to find the sum of the first n terms of an arithmetic sequence?
4. Solve the following arithmetic sequence: 3, 7, 11, 15, ...
5. Determine if the following sequence is arithmetic: 2, 4, 7, 11, ...

Remember to practice finding the nth term and sum of arithmetic sequences to solidify your understanding!