Question

Please answer.....
I'll mark as brainliest

Answer 1

Answer:

1/1024

Step-by-step explanation:

please mark BRAINIEST

Answer 2

Answer:

$\displaystyle \sf \longrightarrow t_{11}=\frac{1}{1024}$

Step-by-step explanation:

Given :

$\displaystyle \sf T_6 = -\frac{1}{32}$

$\displaystyle \sf \longrightarrow T_6 = -2^{-5}$

We know :

$\displaystyle \sf \longrightarrow T_n = a \ r^{n-1}$

$\displaystyle \sf \longrightarrow -2^{-5} = a \ r^{6-1}$

$\displaystyle \sf \longrightarrow -2^{-5} = a \ r^{5} \ ...(i)$

We also have given :

$\displaystyle \sf T_9 = \frac{1}{256}$

$\displaystyle \sf \longrightarrow T_9 = 2^{-8}$

$\displaystyle \sf \longrightarrow 2^{-8} = a \ r^{9-1}$

$\displaystyle \sf \longrightarrow 2^{-8} = a \ r^{8} \ ...(ii)$

Dividing ( ii ) by ( i ) we get :

$\displaystyle \sf \frac{2^{-8}}{-2^{-5}} =\frac{a \ r^{8}}{a \ r^{5}}$

$\displaystyle \sf \longrightarrow r^3=-2^{-3}$

$\displaystyle \sf \longrightarrow r=-2^{-1}$

Putting value of r in ( i ) we get :

$\displaystyle \sf \longrightarrow -2^{-5} = (a). \ -r^{5} \ ...(i)$

$\displaystyle \sf \longrightarrow -2^{-5} = a \ 2^{5} \ ...(i)$

$\displaystyle \sf \longrightarrow a= 1$

Now finding 11th term :

$\displaystyle \sf \longrightarrow t_{11}=1\left(\frac{1}{2}\right)^{11-1}$

$\displaystyle \sf \longrightarrow t_{11}=\left(\frac{1}{2}\right)^{10}$

$\displaystyle \sf \longrightarrow t_{11}=\frac{1}{1024}$

Hence we get required answer.