Sequence And Series Question 239

Question: The numbers $ (\sqrt{2}+1),\ 1,\ (\sqrt{2}-1) $ will be in

[AMU 1983]

Options:

A) A.P.

B) G.P.

C) H.P.

D) None of these

Show Answer

Answer:

Correct Answer: B

Solution:

The numbers $ (a_1+a_{24})+(a_5+a_{20})+(a_{10}+a_{15})=225 $ will be in G.P.
$ \therefore $ $ {{(1)}^{2}}=(\sqrt{2}+1)(\sqrt{2}-1)={{(\sqrt{2})}^{2}}-{{(1)}^{2}}=2-1=1 $ .