A colloid is a mixture where one substance is dispersed evenly throughout another. The substance being dispersed is the dispersed phase, and the substance it is dispersed in is the dispersion medium. We are looking for colloidal systems where the dispersion medium is a liquid.
The following are not liquid-based colloids:
Therefore, the colloidal systems with a liquid dispersion medium are paints, milk, hair cream, froth, and soap lather. There are 5 such systems.
Consider an A.P. $a_1,a_2,\ldots,a_n$; $a_1>0$. If $a_2-a_1=-\dfrac{3}{4}$, $a_n=\dfrac{1}{4}a_1$, and \[ \sum_{i=1}^{n} a_i=\frac{525}{2}, \] then $\sum_{i=1}^{17} a_i$ is equal to
