Question

In a Geometric Progression, 3rd term is 24 and 6th term is 192. Find the 10th term of that Geometric

Progression​

Answer 1

Given

⇒a₃ = 24

⇒a₆ = 192

To Find

⇒a₁₀ = ?

Formula

⇒aₙ = arⁿ⁻¹

Now we get

⇒ar³⁻¹ = 24

⇒ar² = 24           (i)

⇒ar⁶⁻¹ = 192

⇒ar⁵ = 192         (ii)

Now Divide (ii) by(i)

⇒ar⁵/ar² = 192/24

⇒r³ = 8

⇒r =∛(8)

⇒r=2  

Now put the value of r on (ii) eq

⇒ar⁵ = 192

⇒a(2)⁵ = 192

⇒32a = 192

⇒a= 192/32

⇒a= 6

Now we have to find a₁₀

⇒a₁₀ = ar¹⁰⁻¹

Where a = 6 and r = 2

⇒a₁₀ = 6×(2)⁹

⇒a₁₀ = 512×6

⇒a₁₀ = 3072