Post 18: sequences and summation notation

How do we find the terms of a sequence?

Say we were the sequence An = 3n - 2

A1 = 3(1) - 2=1

A2 =3(2)-2=4

....

We must substitute the variable n with the specific term number to find the value of that term.

A recursive sequence

In order to find the terms we have to be given the value of a few terms and also be given the recursive formula

For example

A0=1,A1=1 Ak=Ak-2+Ak-1

 This means that one term is equivalent to the sum of the two before it. 

Therefore

A2=A1+A0=1+1=2

A3=A2+A1=2+1=3

Summation notation

This involved the uppercase of Greek Letter sigma 

Basically it gives the number of terms in a sequence and the pattern. After finding the value for each term, we add them together. We are also given the term we start on.