Sequences and Series
find the geometric means of the following pairs of numbers
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The pth,qthand rthterms of an A.P. are a, b, c, respectively. Show that (q−r)a+(r−p)b+(p−q)c=0.
If pth, qth, rthand sthterms of an A.P. are in G.P. then show that(p−q), (q−r), (r−s)are also in G.P.
How many two–digit numbers are divisible by 3?
Find the sum of the first 15 multiples of 8.
Find the 11thfrom the last term (towards the first term) of the AP : 10, 7, 4, ˙ ˙ ˙, 62.
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 G be A.M. and GM., respectively between two positive numbers, prove that the numbers are A±(A+G)(A−G).
Write the first five terms of the sequence whose nthterms are : an=2n