



 
Hi, Suppose I give you the sequence of numbers
The ... indicates that the pattern is to continue. The pattern I see is that these terms are all 1 divided by a square,
I want an expression that tells you what every term is. I know the terms are 1 over some quantity squared and I am going to call this quantity n. Thus the terms are all 1/n^{2} for some number n. Now I can see what n is, it is the term number
Let's look at a different example
Here what I see is that each term is 4 more than the previous term, so I can write the sequence as
In this case every term after the first is 3 plus some quantity times 4, and this quantity is 1 or 2 or 3 or ... I can make this pattern work, even for the first term if I write the sequence
Thus
In this case the quantity multiplied by 4 is one less than the term number so
I hope this helps,  


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