When `'n'` number of particles of masses `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 find the distance of centre of mass of the system from origin.

Explanation

` x_(cm) = (ma+m(ar)+m(ar^(2))+....+(ar^(n)))/(m+m+m+...+m("n terms "))`
` x_(CM) = (m(a+ar+ar^(2)+....+ar^(n)))/(mn)`
If `r gt 1 ` then
`rArr x_(CM) = 1/n [(a(r^(n)-1))/(r-1)] = (a(r^(n)-1))/(n(r-1))`