MCQ 11 Mark
Assertion (A): If 5 th term of a G.P. is 9 and 11 th term is 16 , then 8 th term is 12 .
Reason (R): In a G.P., $\mathrm{a}_{\mathrm{n}}=\frac{a_{n-k}+a_{n+k}}{2}, \mathrm{n}, \mathrm{k} \in \mathrm{N}$.
Reason (R): In a G.P., $\mathrm{a}_{\mathrm{n}}=\frac{a_{n-k}+a_{n+k}}{2}, \mathrm{n}, \mathrm{k} \in \mathrm{N}$.
- ABoth A and R are true and R is the correct explanation of A .
- BBoth A and R are true but R is not the correct explanation of A.
- C$A$ is true but $R$ is false.
- DA is false but $R$ is true.
Answer
View full question & answer→A is true but R is false.
Explanation: We know that in a G.P.
$a_{n}=\sqrt{a_{n-k} \cdot a_{n+k}}$
$\therefore$ Reason is false.
Given $\mathrm{a}_{5}=9$ and $\mathrm{a}_{11}=16$.
So, $a_{8}=\sqrt{a_{8-3} \times a_{8+3}}$
$\Rightarrow a_{8}=\sqrt{9 \times 16}=\sqrt{144} \Rightarrow a_{8}=12$
$\therefore$ Assertion is true.
Explanation: We know that in a G.P.
$a_{n}=\sqrt{a_{n-k} \cdot a_{n+k}}$
$\therefore$ Reason is false.
Given $\mathrm{a}_{5}=9$ and $\mathrm{a}_{11}=16$.
So, $a_{8}=\sqrt{a_{8-3} \times a_{8+3}}$
$\Rightarrow a_{8}=\sqrt{9 \times 16}=\sqrt{144} \Rightarrow a_{8}=12$
$\therefore$ Assertion is true.