Find the sum of the G.P.:
2/5, 2/25, 2/125, 2/625, … to the n terms.

a) 5/4(1-(1/5ⁿ))
b) 2/5(1-(1/5ⁿ))
c) 1/2(1-(1/5ⁿ))
d) 4/5(1-(1/5ⁿ))

Answer : c) 1/2(1-(1/5ⁿ))

UP Police SI Paper – Numerical Mental Ability

Solution :

To find the sum of the given geometric progression (G.P.), we need to identify the first term and the common ratio.
The first term ( a ) is 2/5
The common ratio ( r ) is found by dividing the second term by the first term:

The sum of the first ( n ) terms of a G.P. is given by the formula:

Substituting the values of ( a ) and ( r ):

So, the sum of the first ( n ) terms of the given G.P. is: