Sum To n Terms Of a GP - Practice Questions & MCQ

Sum of n-term of a GP

Let S_n be the sum of n terms of the G.P. with the first term ‘a’ and common ratio ‘r’. Then 

The above formula does not hold for r = 1

For r = 1, each of the n terms is equal to a, and thus the sum of n terms of the G.P. is .

Sum of an infinite GP   

If a is the first term and r is the common ratio of a G.P. Then,

Let, - 1 < r < 1, i.e. | r | < 1, then 

[as this is infinite G.P., so n tends to infinity] 

is the sum to infinite terms of the G.P.

Note: If r ≥ 1, then the sum of an infinite G.P. tends to infinity. 

Application of GP

To write a non-terminating repeating number in p/q form:

Example:

The value of 0.358585858585..........

Application of GP

The sum of n-term of the series is

The sum of n-term of the series   is