Arithmetic Sequences: Algebra


a1=First Term

n=Term Number in Sequence

d=Common Difference (Number Added/Subtracted to each Term in Sequence)

Hi everyone and welcome to Mathsux! In this post, we’re going to go over arithmetic sequences. We’ll see what arithmetic sequences are, break down the formula an=a1+(n-1)d, and solve two different types of examples. As always if you want more questions, check out the video below and the practice problems at the end of this post. Happy calculating! 🙂

What are Arithmetic Sequences?

Arithmetic sequences are a sequence of numbers that form a pattern when the same number is either added or subtracted to each subsequent term.


arithmetic sequences

Notice we are adding 2 to each term in the sequence above. If the pattern were to continue, the next term of the sequence above would be 12. This is an arithmetic sequence!

In the above sequence it’s easy to see what the next term is, but what if we wanted to know the 123rd term?  That’s where the Arithmetic Sequence Formula comes in!

Arithmetic Sequence Formula:

arithmetic sequences

Now that we know the arithmetic sequence formula, let’s try to answer our original question below:

arithmetic sequence examples

-> First, let’s write the arithmetic sequence formula:

arithmetic sequences

-> Fill in our formula and solve with the given values.

Now let’s look at another example where we subtract the same number from each term in the sequence, making the common difference negative.

arithmetic sequence examples

-> First let’s identify the common difference between each number in the sequence. Notice each term in the sequence is being subtracted by 3.

arithmetic sequences

-> Now let’s write out our formula:

arithmetic sequences

-> Next let’s fill in our formula and solve with the given values.

Practice Questions:

  1. Find the 123rd term given the following sequence: 8, 12, 16, 20, 24, ….
  2. Find the 117th term given the following sequence: 2, 2.5, 3, 3.5, …..
  3. Find the 52nd term given the following sequence: 302, 300, 298, …..
  4. A software engineer charges $100 for the first hour of consulting and $50 for each additional hour.  How much would 500 hours of consultation cost?


Still got questions? No problem! Don’t hesitate to comment with any questions or check out the video above. Happy calculating! 🙂

Also, if you’re looking to learn more about Sequences, check out these posts on Geometric Sequences and Recursive Formulas!

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