In a G.P., the $3^{\text {rd}}$ term is 24 and the $6^{\text {th}}$ term is 192. What is its $10^{\text {th}}$ term?

3072

Let the first term is a and the common ratio is r

Then,

ar²= 24 ........... (i)

and ar⁵= 192 ........... (ii)

Dividing (ii) by (i), we get

ar⁵/ar² = 192/24

r³ = 8

r = 2

Now,

ar² = 24

⇒a × 2² = 24

⇒a = 6

Thus the 10th term will be ar⁹ = 6×2⁹ = 3072