When `n` number of particles each of mass `m` are at distances `x_(1)=a, x_(2)=ar, x_(3)=ar^(2)…….x_(n)=ar^(n)` units from origin on the x-axis, then the distance of their centre of mass from origin.

Explanation

To find the distance of the center of mass of `n` particles, each of mass `m`, located at distances `x_1 = a`, `x_2 = ar`, `x_3 = ar^2`, ..., `x_n = ar^(n-1)` from the origin on the x-axis, we can follow these steps:

### Step-by-step Solution:

1. **Identify the Positions of the Particles**:
The positions of the particles are given as:
- Particle 1: \( x_1 = a \)
- Particle 2: \( x_2 = ar \)
...