CBSE Class 11-science Answered
if x,y,z are in ap ,x,xy,z are in a gp show that x,x^2(square)y,z are in hp
Asked by | 15 Aug, 2012, 07:04: PM
Expert Answer
Given, x,y,z are in A.P.
Therefore, x+z = 2y ......(1)
Also, x,xy,z are in G.P
Therefore, (xy)2 = xz
x2y2 = xz
xy2 = z ....(2)
Next, we have to prove that x,x2y,z are in H.P
Now, 1/x+1/z = (z+x)/xz
= 2y/x.xy2 [Using (1) and (2)]
= 2/x2y
Therefore, 1/x+1/z =2/x2y
Therefore,x,x2y,z are in H.P
Answered by | 20 Aug, 2012, 07:58: PM
Application Videos
-
Sum of infinite terms of an Arithmetic-Geometric Progre ...
Video contains the question based on how to find the sum of infinite terms ...
Concept Videos
-
Concepts of sequence and series - Introduction
Introduce the concept of sequences and series, their types and specific typ... -
Arithmetic Progressions
This video covers examples on condition for a sequence to be an arithmetic ... -
Relationship between A.M. and G.M.
This video explains the geometric Mean of two numbers and inserting numbers... -
Special Sequences and Series
This video covers examples related to Summation of a series containing squa... -
Arithmetic Mean
This video explains the arithmetic mean of two numbers, inserting n numbers...
CBSE 11-science - Maths
Asked by cubesneha.2005 | 07 Feb, 2024, 12:55: AM
ANSWERED BY EXPERTCBSE 11-science - Maths
Asked by hridayjayaram085 | 31 Jan, 2024, 10:53: PM
ANSWERED BY EXPERTCBSE 11-science - Maths
Asked by prashantbharati75 | 29 Sep, 2023, 09:30: AM
ANSWERED BY EXPERTCBSE 11-science - Maths
Asked by Bhaveshkr211 | 30 Jul, 2023, 05:20: PM
ANSWERED BY EXPERTCBSE 11-science - Maths
Asked by sakshirana374 | 24 Jul, 2022, 05:39: PM
ANSWERED BY EXPERTCBSE 11-science - Maths
Asked by sanjuktamukherjee165 | 24 Oct, 2021, 11:04: AM
ANSWERED BY EXPERTCBSE 11-science - Maths
Asked by rahulksinha200 | 16 Oct, 2021, 02:08: PM
ANSWERED BY EXPERTCBSE 11-science - Maths
Asked by Vibhorjarora798 | 21 Aug, 2021, 05:43: PM
ANSWERED BY EXPERTCBSE 11-science - Maths
Asked by shivangkarol | 16 Jun, 2021, 01:18: PM
ANSWERED BY EXPERT
