R D Sharma Solutions for Chapter: Geometric Progressions, Exercise 5: EXERCISE 20.5

If a, b, c are in G.P., prove that:

$\left(a+2b+2c\right)\left(a-2b+2c\right)=a^2+4c^2$

If $a,b,c,d$ are in G.P., prove that:

${\left(a+b+c+d\right)}^2={\left(a+b\right)}^2+2{\left(b+c\right)}^2+{\left(c+d\right)}^2$

If $a.b,c,d$ are in G.P., prove that:

$(\mathrm{b}+\mathrm{c})(\mathrm{b}+\mathrm{d})=(\mathrm{c}+\mathrm{a})(\mathrm{c}+\mathrm{d})$

If a, b, c are in G.P., prove that the following are also in G.P.:

$a^3,b^3,c^3$

If a, b, c are in G.P., prove that the following are also in G.P.:

${\mathrm{a}}^2+{\mathrm{b}}^2,\mathrm{ab}+\mathrm{bc},{\mathrm{b}}^2+{\mathrm{c}}^2$

If $a,b,c,d$ are in $G.P.$, prove that:

$(a^2-b^2),(b^2-c^2),(c^2-d^2)$ are in G.P.

If $a,b,c,d$ are in $G.P.$, prove that: $\frac{1}{a^2+b^2},\frac{1}{b^2+c^2},\frac{1}{c^2+d^2}$ are in G.P.

If $a,b,c,d$ are in $G.P.$, prove that:

$(a^2+b^2+c^2),(ab+bc+cd),(b^2+c^2+d^2)$ are in $G.P.$