Mathematicians have found ways that enable us to determine numbers in sequences easily.
They derive formulas to suit certain types of number sequences.
For example, the number sequence 5, 7, 9, 11, 13, 15 … is known as an arithmetic progression with common difference of 2.
To find the sum of numbers in a sequence 5, 7, 9, 11, 13, 15 …, we can use the following:
(from wikipedia: http://en.wikipedia.org/wiki/Arithmetic_progression)
On the other hand, if we have another number sequence, 1^2, 2^2, 3^3, .....
we can find the sum of the square numbers using the formula: