= 3 x 3 x 3 x 3 x 3
= 243- Finite GP
A GP whose last term is known is said to be a finite GP.
Eg. : 1, 2, 4, 8, 16, ... 256
Here the last term is known and hence it is a finite GP. - Infinite GP
A GP whose last term is not known is said to be an infinite GP.
Eg. : 1, 3, 9, 27, 81, ...
Here the last term is not known and hence it is an infinite GP. - Sum of the terms of a GP
The sum of the first ‘n’ terms of a GP can be found using the formulae:
Sn = a(rr 11 )n
−− if r > 1= a( 11 rr)n
−− if r < 1= na if r = 1
Usually, the formulae may be memorized. In order to understand the structure of the
formulae, they can be presented in both linear and spatial forms.- Sum of the first ‘n’ natural numbers
The sum of the first ‘n’ natural numbers can be found by using the formula,
1+2+3+4+5+6+ ... + n = n(n 2 +^1 )
where ‘n’ is the number of terms in the sequence.- Sum of the squares of the first ‘n’ natural numbers
The sum of the squares of the first ‘n’ natural numbers is found by the formula,