If 1b−c,1c−a,1a−bbe consecutive terms of an AP, then (b−c)2,(c−a)2,(a−b)2 will be in

# If $\frac{1}{\mathrm{b}-\mathrm{c}},\frac{1}{\mathrm{c}-\mathrm{a}},\frac{1}{\mathrm{a}-\mathrm{b}}$be consecutive terms of an AP, then $\left(\mathrm{b}-\mathrm{c}{\right)}^{2},\left(\mathrm{c}-\mathrm{a}{\right)}^{2},\left(\mathrm{a}-\mathrm{b}{\right)}^{2}$ will be in

1. A

GP

2. B

AP

3. C

HP

4. D

none of these

Register to Get Free Mock Test and Study Material

+91

Verify OTP Code (required)

### Solution:

Now,  we assume $\left(\mathrm{b}-\mathrm{c}{\right)}^{2},\left(\mathrm{c}-\mathrm{a}{\right)}^{2},\left(\mathrm{a}-\mathrm{b}{\right)}^{2}$ are in AP, then we have

Also,if  $\frac{1}{\mathrm{b}-\mathrm{c}},\frac{1}{\mathrm{c}-\mathrm{a}},\frac{1}{\mathrm{a}-\mathrm{b}}$ are in,AP, then

which is equal to Eq.(i), so our hypothesis is true.

Register to Get Free Mock Test and Study Material

+91

Verify OTP Code (required)