Question

The numbers $\sqrt{2}+1,1,\sqrt{2}-1$ will be in

• A. A.P
• B. G.P
• C. H.P
• D. None of these

Answer 1

The correct option is B

G.P

Identify the type of mathematical progression for the given terms

Let $a=\sqrt{2}+1$, $b=1$, $c=\sqrt{2}-1$

Check the condition for arithmetic progression

$2b=a+c$

$2b=2$

$a+c=\sqrt{2}+1+\sqrt{2}-1=2\sqrt{2}$

$\therefore$ $2b\ne a+c$

Condition for arithmetic progression is not satisfied.

Check the condition for geometric progression

$b^2=ac$

$b^2=1$

$ac=\left(\sqrt{2}+1\right)\left(\sqrt{2}-1\right)=2-1=1$

$\therefore$ $b^2=ac$

Condition for geometric progression is satisfied.

$\sqrt{2}+1,1,\sqrt{2}-1$ are in a geometric progression,

Hence option $\left(B\right)$ is the correct answer.