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
- n = 50
- = 12
- = -135
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.