Number Series

Number Series

Some Basic Formula:

(a + b)(a - b) = (a2 - b2)

(a + b)2 = (a2 + b2 + 2ab)

(a - b)2 = (a2 + b2 - 2ab)

(a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca)

(a3 + b3) = (a + b)(a2 - ab + b2)

(a3 - b3) = (a - b)(a2 + ab + b2)

(a3 + b3 + c3 - 3abc) = (a + b + c)(a2 + b2 + c2 - ab - bc - ac)

When a + b + c = 0, then a3 + b3 + c3 = 3abc.

The nth Term

The 'nth' term is a formula with 'n' in it which enables you to find any term of a sequence without having to go up from one term to the next.

Constant Difference Sequences:

nth term = dn + (a - d)
Where d is the difference between the terms, a is the first term and n is the term number.

Changing Difference Sequences:

nth term = a + (n - 1)d + ½(n - 1)(n - 2)c
Where d is the difference between the terms, a is the first term and n is the term number
This time there is a letter c which stands for the second difference (or the difference between the differences and d is just the difference between the first two numbers.

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