In a G.P. the 3^(rd) term is 24 and 6^(th) term is 192 then 10^(th) term is ……………………. 

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.

Correct option is B) 3072