This week was the first week of Pre Calculus 11 for me. So far it has been good, as we are learning about series and sequences. Today I am going to teach you the difference between arithmetic sequences and an arithmetic series. I will also show the formula to find the nth-term and how to find the sum of the terms. STAY TUNED 🙂

A** SEQUENCE** for example, is a set of numbers that are changing in some way.

ex/ 5, 10, 20, 40, 80

5 is called , 10 = , 15 = and so on. The t stands for term.

An **ARITHMETIC SEQUENCE** is a sequence that changes by a constant amount. The constant amount is also known as the common difference.

ex/ 5, 10, 15, 20, 25, d=+5 ;The common difference is +5

to find the common difference the formula is –

NOT ARITHMETIC, NO CONSTANT DIFFERENCE

An **ARITHMETIC SERIES **is the terms of an arithmetic sequence added together. The point is to find the sum of the desired terms.

ex/ 5+10+15+20+25 = 75

**How to find the nth-term**

Say you wanted to find what is in the sequence 12, 9, 6, 3, 0 is but you don’t want to continue writing the whole sequence out. Well your in luck, there is a fast way.

**The formula to find the nth-term is = + d(n-1)**

- The nth-term is =
- d= -3
- = 12

Now we insert all the known numbers into the formula

- = + d(n-1)
- = 12 + (-3)(50-1)
- = 12 + (-3)(49)
- = 12 -147
- = -135

There you are, you just figure out how to find the 50th term quick and easy.

**How to find the sum of a series**

We will take the example from above and determine the sum of . means to will be added.

The formula to determine the sum is

Insert into formula

There you have it. Today you learned what an arithmetic sequence and series were, what the formula to find the nth-term and the sum of a series was, and how to solve. I hope this blog post helps you in your future with practice and studying.