Question

In a sequence of $21$ terms, the first $11$ terms are in $A.P$. with common difference $2$ and the last $11$ terms are in $G.P$. with common ratio $2$. If the middle term of the $A.P$. is equal to the middle term of the $G.P$., then the middle term of the entire sequence is

• A. $-10 / 31$
• B. $10 / 31$
• C. $32 / 31$
• D. $-31 / 32$

Answer 1

Answer: (A)

Middle term of $A.P$. = Middle term of $G.P$.
$\Rightarrow a+10=(a+20) 2^{5}$
$\Rightarrow -31 a=630 \Rightarrow a=-630 / 31$
Now, middle term of entire sequence
$=a+20=-\frac{630}{31}+20=-\frac{10}{31}$