Determine the 12th term of a G.P. whose 8th term is 192 and common ratio is 2.

Given, a₈ = 192 and r = 2.

By formula, a_n = ar^{n - 1}.

⇒ a₈ = a(2)^{(8 - 1)}
⇒ 192 = a(2)⁷
⇒ a = $\dfrac{192}{2^7} = \dfrac{192}{128} = \dfrac{3}{2}.$

12th term of the G.P. is a₁₂,

$\Rightarrow a${12} = \dfrac{3}{2}(2)^{12 - 1} \\[1em] \Rightarrow a{12} = \dfrac{3}{2} \times 2^{11} \\[1em] \Rightarrow a{12} = 3 \times 2^{10} \\[1em] \Rightarrow a{12} = 3 \times 1024 \\[1em] \Rightarrow a_{12} = 3072.

Hence, the 12th term of the G.P. is 3072.