Question

In a G.P., the 3rd term is 24 and the 6th term is 192. Find the 12^th term.
1. 2 × 211
2. 3 × 211
3. 6 × 212
4. 6 × 211

Answer 1

Correct Answer - Option 4 : 6 × 211

Concept:

Geometric Progression (GP): The series of numbers where the ratio of any two consecutive terms is the same, is called a Geometric Progression.

​A Geometric Progression of n terms with first term a and common ratio r is represented as:

a, ar, ar², ar³, ..., ar^n-2, ar^n-1.

 

Calculation:

Given: the 3rd term is 24 and the 6th term is 192

T₃ = ar² = 24          ...(1)

T₆ = ar⁵ = 192          ...(2)

Dividing equation (2) by (1), we get:

r³ = 8

⇒ r = 2

Using equation (1), a = 24/2² = 6.

The 12th term = T₁₂ = 6 × 2¹¹ = 12288.