Questions
Find the two numbers whose AM and GM are given below: Also, verify the result using relations greater number = $\rm AM + \sqrt {AM^2 - GM^2}$ and smaller number = $\rm AM - \sqrt {AM^2 - GM^2}$
- AM = 25 and GM = 24
- AM = 29 and GM= 2I
- AM = 41 and GM = 40
- AM = 37 and GM = 35
2k, 2k+3, and 2k+9 are the first three terms of a geometric sequence. Find the $\rm 6^{th}$ term.
3x, x+6, and 3x+8 are the first three terms of a geometric sequence. Find the $\rm 4^{th}$ term.
p+9, p-6, and 4 are the first three terms of a geometric sequence. Find the $\rm 5^{th}$ term.
The AM of two numbers is 25 and their GM is 20. Find the numbers.
The AM of two numbers is 34 and their GM is 16. Find the numbers.
The arithmetic mean of two numbers is 15 and their geometric mean is 9. Find the numbers.
4 geometric means are inserted between a and b. If the first and third means are 54 and 24 respectively, find the values of a and b.
There are 5 geometric means between a and b. If the second mean and last mean are 63 and 1701 respectively, find the values of a and b.
How many geometric means are there between 10 and 1280, where the ratio of the first mean is to the last mean is as 1 : 32?