**What is an Arithmetic Sequence or an Arithmetic Progression?**

Arithmetic progression is a sequence in which difference between any two consecutive terms is constant.

For example, we have sequence: 5, 8, 11, 14, 17, 20, 23.

The difference between any two consecutive terms is 3.

{ and }

**The first term of arithmetic progression is represented by small letter a and difference between any two consecutive terms (which is constant) is represented by small letter d**.

The difference between any two consecutive terms is called common difference because it is constant for any two consecutive terms.

Now, if you are given any sequence, Can you determine if it is an arithmetic sequence (progression)?

- Can you determine if 5, 10, 15, 20, 25, 30 is an arithmetic sequence?

Yes, it is an arithmetic sequence because difference between any two consecutive terms is constant which is equal to 5. Note that we always subtract previous term from the chosen term to find common difference.

{ and }

- Is the following sequence arithmetic?

5, 8, 10, 13, 16.

No, it is not an arithmetic sequence because difference between any two consecutive terms is not same. Here, 8-5 = 3 but 10-8 = 2.

- Can you identify if the following sequence is arithmetic. If, it is arithmetic then find its first term and common difference.

-4, -8, -12, -16, -20.

Yes, it is an arithmetic sequence because difference between any two consecutive terms is constant.

{}

{}

**First term = a = -4**

**Common difference = d= -4**

Check video for better understanding