Question
Download Solution PDFIn a G.P., the 3rd term is 24 and the 6th term is 192. Find the 12th term.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
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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