- Home
- Standard 11
- Mathematics
8. Sequences and Series
medium
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
A
$A.P.$
B
$G.P.$
C
$H.P.$
D
None of these
Solution
(b) 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 $G.P.$
Standard 11
Mathematics
