Question

The 6th term of GPis -1/32 and 9th term is 1/256 then 11th term is ?

Answer 1

first term is equal to a ® ans=1/1024

Answer 2

Solution:

The nth term of Geometric progression,proceeding in the way,$a,ar, ar^2, ar^3, ar^4,.....$  is given by $=ar^{n-1}$.

$a_{6}=\frac{-1}{32}\\\\ a_{9}=\frac{1}{256}\\\\ ar^5=\frac{-1}{32}\\\\ ar^8=\frac{1}{256}$

$\frac{a_{9}}{a_{6}}=\frac{ar^8}{ar^5}=\frac{\frac{1}{256}}{\frac{-1}{32}}\\\\ r^3=\frac{-1}{8}\\\\ r=\frac{-1}{2}$

Substituting , $r=\frac{-1}{2} {\text{in }} a_{6}, {\text{we get}}, a=1.$

$a_{11}=ar^{10}\\\\a_{11}=1 \times [\frac{-1}{2}]^{10}=\frac{1}{2^{10}}$