Discussion
Let \(G_{1}, G_{2}, G_{3}\) be geometric means between \(l\) and \(n\), where \(l\) and \(n\) are positive real numbers.Then the common ratio is
Answer: D
The common ratio is \(\left(\frac{n}{l}\right)^{1/4}\).
Inserting three geometric means gives the five-term G.P. \(l, G_{1}, G_{2}, G_{3}, n\), so n is the fifth term and is reached after four ratios.
\[ n = lr^{4} \Rightarrow r = \left(\frac{n}{l}\right)^{1/4} \]
The exponent 1/3 counts the three means instead of the four gaps between five terms, and 1/2 is the ratio for a single mean. \(\frac{n}{l}\) and its square are the ratio of the end terms, not of consecutive terms.
No comment is present. Be the first to comment.
Loading…
Post your comment
Please log in or register to post a comment.
Examination Categories
- SSC Exams
- Banking Exams
- Teaching Exams
- Civil Services Exams
- Railways Exams
- Engineering Recruitment Exams
- Defence Exams
- State Government Exams
- Police Exams
- Insurance Exams
- Nursing Exams
- Other Government Exams
- NRA CET
- PG Entrance Exams
- Campus Placement
- MBA Entrance Exams
- CUET and UG Entrance
- Judiciary Exams
- Regulatory Body Exams
- Software Development