If it's an arithmetic sequence like

3, 7, 11, 15, ...

Then the first term, 3, is called , the second term, 7, is called 
, etc.  The common difference is the amount that's added to each
number to get the next one. To get from 3 to 7 you add 4. To get from 7 to 11
you add 4, to get from 11 to 15 you add 4.  So 4 is the common difference d

The get the equation for the nth term, you use the formula












and to get the sum of the first n terms :













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f it's a geometric sequence like

4, 12, 36, 108, ...

Then the first term, 3, is called , the second term, 12, is called 
, etc.  The common ratio is the amount that each number is
multiplied by to get the next one. To get from 4 to 12 you multiply by 3. To 
get from 12 to 36 you multiply by 3, to get from 36 to 108 you multiply by 3.  
So 3 is the common ratio r.

The get the equation for the nth term, you use the formula





and to get the sum of the first n terms :









Edwin