Sequence And Series Question 207
Question: If $ a,\ b,\ c $ are in A.P. and $ a,\ b,\ d $ in G.P., then $ a,\ a-b,\ d-c $ will be in
[Ranchi BIT 1968]
Options:
A) A.P.
B) G.P.
C) H.P.
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
Given that $ a,\ b,\ c $ are in A.P.
$ \Rightarrow b=\frac{a+c}{2} $ ?..(i) and $ b^{2}=ad $ ?.. (ii) Hence $ a,\ a-b,\ d-c $ are in G.P. because $ {{(a-b)}^{2}}=a^{2}-2ab+b^{2}=a(a-2b)+ad $ $ =a(a-a-c)+ad=ad-ac $ .
BETA
