Question

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Answer 1

Given, 8th term = 192, Common ratio = 2.

Now,

8th term = 192.

⇒ a₈ = ar⁸⁻¹

⇒ 192 = a(2)⁷

⇒ 192 = a * 128

⇒ 192/128 = a

⇒ 3/2 = a.

12th term:

⇒ a₁₂ = ar¹²⁻¹

         = ar¹¹

         = (3/2) * (2)¹¹

          = 3 * 1024

          = 3072.

Therefore,12th term of the GP is 3072.

Hope it helps!

Answer 2

Give 8th term = 192 and the common ratio =2
a
$a8 = a{r} {}^{(8 - 1)} { } \\ 192 = a(2) {}^{7} \\ 192 = a \times 288 \\ a \: = \frac{288}{192} \\ a \: = \frac{3}{2} \\12th term \\ a12 = \: ar {}^{(12 - 1)} \\ = \frac{3}{2} \times (2) {}^{11} \\ = 3 \times 1024 = 3072$