Arithmetic sequences
1.0 arithmetic sequence
what is an arithmetic sequence?
a arithmetic sequence is simply a sequence of numbers in which every number is bigger than the previous number by the same amount.
for example 1,2,3,4,5 or 2,4,6,8 or 1.0, 1.5, 2.0, 2.5
the numbers in a arithmetic sequence don't have to increase, 1, 0, -1, -2
is also a arithmetic sequence.
exs:which of the following are arithmetic sequences?
1. 1,2,3,4,5...
2. 62,48,34,20,4...
3. 1,4,7,10...
when we add up all the terms of an arithmetic sequence the result is a series.
We call the first term of the sequence a.
The difference (between the terms) is called d.
knowing that, an arithmetic sequence looks like this:
a, a+d, a+2d, a+3d, ...
the nth term is a+(n-1)d where n is the number of terms.
The formula for the sum of the first n terms of an arithmetic sequence is:
(2a + (n-1)d)(n/2)
another pointer:
suppose that i wanted to tell you that the ninth term of an arithmetic series if 9, I could writing
a + 8d =9 or a9=9
also instead of writing "find the sum of the first 15 terms" you can write "find S11
This is the basic knowledge that will help you a lot.
Now you are ready to solve some arithmetic sequence problems!!
back
home