Sequence And Series Question 250
Question: An A.P., a G.P. and a H.P. have the same first and last terms and the same odd number of terms. The middle terms of the three series are in
Options:
A) A.P.
B) G.P.
C) H.P.
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
Let $ a $ and $ b $ be the same first and last terms of the three progressions, each having $ (2n+1) $ terms. Then the middle term of the A.P. is $ \frac{a+b}{2} $ . The middle term of the G.P. is $ \sqrt{ab} $ . The middle term of the H.P. is $ \frac{2ab}{a+b} $ . Obviously, these terms are in G.P.
BETA
