In a G.P., the 3rd term is 24 and the 6th term is 192. Find the 12th term.

  1. 2 × 211
  2. 3 × 211
  3. 6 × 212
  4. 6 × 211

Answer (Detailed Solution Below)

Option 4 : 6 × 211
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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, ..., arn-2, arn-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.

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