The sums of first $\mathrm{n}$ terms of two $\mathrm{A}.\mathrm{P}.$’s are in the ratio $\left(7\mathrm{n}+2\right):\left(\mathrm{n}+4\right)$. Find the ratio of their $5\mathrm{th}$ terms.

If $\frac{1}{\mathrm{a}},\frac{1}{\mathrm{b}},\frac{1}{\mathrm{c}}$ are in A.P

Prove that: $\frac{\mathrm{b}+\mathrm{c}}{\mathrm{a}},\frac{\mathrm{c}+\mathrm{a}}{\mathrm{b}},\frac{\mathrm{a}+\mathrm{b}}{\mathrm{c}}$ are in A.P.

If $\frac{1}{\mathrm{a}}, \frac{1}{\mathrm{b}}, \frac{1}{\mathrm{c}}$ are in A.P.,

Prove that: $\mathrm{a}\left(\mathrm{b}+\mathrm{c}\right), \mathrm{b}\left(\mathrm{c}+\mathrm{a}\right), \mathrm{c}\left(\mathrm{a}+\mathrm{b}\right)$ are in A.P.