Correct option is (B) 3072
In G.P., \(a_3=24,a_6=192\)
Let first term of the G.P. is a & common ratio of the G.P. is r.
\(\therefore ar^2=24\) ____________(1) \((\because a_3=ar^2)\)
& \(ar^5=192\) ____________(2) \((\because a_6=ar^5)\)
\(\therefore\frac{ar^5}{ar^2}=\frac{192}{24}=8\) (From (1) & (2))
\(\Rightarrow r^3=8=2^3\)
\(\therefore r=2\)
Put r = 2 in equation (1), we get
\(a.2^2=24\)
\(\Rightarrow a=\frac{24}4=6\)
\(\therefore a_{10}=ar^9=6(2)^9\)
\(=6\times512=3072\)
Hence, \(10^{th}\) term of given G.P. is 3072.
