Part 1
This week, I have learned how to solve arithmetic sequence and series. Before we begin, we must learn some vocabulary to be able to solve these questions.
Arithmetic sequence: is a sequence of number that the difference between the consecutive terms is constant. Ex: The sequence 1 ,3, 5, 7, 9, … is an arithmetic progression with common difference of 2.
General term: To determine an expression for the general term, we use . To find what is , we use this formula:
If we have a sequence going, -3, 2, 7, 12…
-3 = , 2= t_2$, 7 = and so on.
The letter “n” is the number of term is needed to get to the number you are looking for. The letter “d” is the common difference between numbers. To determine “d” you can use this formula:
Now to begin, I’ll go through the whole formula step by step.
If we have the sequence of
10, 20, 30, 40, 50… ,
and the question is asking for the 50th term, we will begin by finding the common difference.
Common difference (d) = +10 each time.
Next, we would put everything in the formula.
As a result, is 500.
Part 2
Second part of this blog is how to find the series. Again lets go through some vocabulary.
Series: Is the sum of the terms in an arithmetic sequence.
Ex:
The arithmetic sequence 5, 8, 11, 14
The arithmetic series 5+8+11+14
The term is to represent the sum of the first “n” terms of a series.The nth term of an arithmetic series is the nth term of the related arithmetic sequence.
=
=
= +
= +
Now, we can begin to find the series of my sequence
10, 20, 30, 40, 50,
However, we don’t know the formula to find .
Formula to find .
Lets solve this problem. We will try to find the 50th term.
In conclusion, you have learned to find the arithmetic sequence and the arithmetic series. Stay tune for next week as I learn different a math during class.