Algebra Definition and Examples
Algebra Definition and Examples
ALGEBRA
Sum of first n natural numbers = n(n+1)/2
Sum of the squares of first n natural numbers = n(n+1)(2n+1)/6
Sum of the cubes of first n natural numbers = [n(n+1)/2]2 Sum of first n natural odd numbers = n2
Average = (Sum of items)/Number of items
Arithmetic Progression –
An A.P. is of the form a, a+d, a+2d, a+3d, …
where a is called the ‘first term’ and d is called the ‘common difference’nth term of an A.P. tn = a + (n-1)d
Sum of the first n terms of an A.P. Sn = n/2[2a+(n-1)d] or Sn = n/2(first term + last term)
Geometrical Progression (G.P) –
A G.P. is of the form a, ar, ar2, ar3, …
where a is called the ‘first term’ and r is called the ‘common ratio’.nth term of a G.P. tn = arn-1
Sum of the first n terms in a G.P. Sn = a|1-rn|/|1-r|
