Sequences and Series
If a,b,c,d,e are five positive numbers then
The sum of two numbers is 6 times their geometric means, show that numbers are in the ratio (3+22):(3−22).
The ratio of the A.M. and G.M. of two positive numbers a and b, is m : n. Show that a : b = (m+m2−n2):(m−m2−n2).
In a school students thought of planting trees in and around the school to reduce air pollution. It was decided that the number of trees, that each section of each class will plant, will be the same as the class, in which they are studying, e.g., a section of Class I will plant 1 tree, a section of Class II will plant 2 trees and so on till Class XII. There are three sections of each class. How many trees will be planted by the students?