Sequences and Series
Insert x arithmetic means between x2 and 1.
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?
If a and b are the roots of x2−3x+p=0 and c, d are the roots x2−12x+q=0 where a,b,c,d form a G.P. Prove that (q+p):(q−p)=17:15.