Math 11 Sequences and Series Blog Post

In the first day of Math class, we study about Arithmetic sequences. 

This is simple patterns like these ones:

here is the term, each term are being counted and it has relevancy keeping the numbers like the picture

Ex: T1=2 (t1 is block 1), T2=5(T2 is block 2), T3=8(block 3)……. So you can see the term is bigger so we know that the sequences of this term are “PLUS”. it mean T1=1, T2=5 so if you want to have T2 you need to plus number before T2 with 3: T2=T1 + 3=5

T3=T2 + 3=8. with the above comments, we have this formula:

that is what we call Arithmetic sequences

Second units are Arithmetic Series.

Is the term of an arithmetic sequence is added, the result

for example

3,5,7,9,11 —–> Arithmetic sequences

3+5+7+9+11 —–> Arithmetic series

We have the formula:

Third units are Geometric Sequences

It is a sequences in which each term after the first obtained by multiplying the preceding term by a fixed nonzero real number called common ratio. The sequences discussed in the last slide

We have the formula:

 

fourth units are Infinite Geometric Series

 

The formula for the sum of a geometric series is When r is less then 1 we use this equivalent equation