If a ,b ,c are in G.P. and x ,y are the ...

If `a ,b ,c` are in G.P. and `x ,y` are the arithmetic means of `a ,ba n db ,c` respectively, then prove that `a/x+c/y=2a n d1/x+1/y=2/b`

A

`a/x +c/y =2`

B

`1/x + 1/y = 3/b`

C

`a/x + c/y =1`

D

`1/x + 1/y =1/b`

Text Solution

Verified by Experts

The correct Answer is:

A

Topper's Solved these Questions

SEQUENCE AND SERIES
VMC MODULES ENGLISH|Exercise LEVEL-2|34 Videos
SEQUENCE AND SERIES
VMC MODULES ENGLISH|Exercise JEE MAIN & Advance ( ARCHIVE)|46 Videos
SEQUENCE AND SERIES
VMC MODULES ENGLISH|Exercise JEE MAIN & Advance ( ARCHIVE)|46 Videos
REVISION TEST-2 JEE
VMC MODULES ENGLISH|Exercise MATHEMATICS|25 Videos
STRAIGHT LINES
VMC MODULES ENGLISH|Exercise JEE Advanced Archive (State true or false: Q. 42)|1 Videos

Similar Questions

Explore conceptually related problems

If a, b, c are in G.P . and x, y are arithmetic means of a, b and b, c respectively, then (1)/(x)+(1)/(y) is equal to

If a, b, c are in G.P., x and y are the A.M.'s of a, b and b, c respectively, then prove that: (i)(a)/(x)+(c)/(y)=2" "(ii) (1)/(x)+(1)/(y)=(2)/(b)

If a ,b , a n dc are in G.P. and x ,y , respectively, are the arithmetic means between a ,b ,a n db ,c , then the value of a/x+c/y is 1 b. 2 c. 1//2 d. none of these

If a ,b ,a n dc are in G.P. and x a n d y , respectively, be arithmetic means between a ,b ,a n db ,c ,t h e n (a) a/x+c/y=2 b. a/x+c/y=c/a c. 1/x+1/y=2/b d. 1/x+1/y=2/(a c)

If a, b and c are in G.P and x and y, respectively , be arithmetic means between a,b and b,c then

If a,b,c are in G.P. and x,y be the AM's between a,b and b,c respectively then (A) 1/a+1/b=(x+y)/6 (B) ax+cy=b (C) a/x+c/y=2 (D) 1/x+1/y=2/b

If x, y, z are in arithmetic progression and a is the arithmetic mean of x and y and b is the arithmetic mean of y and z, then prove that y is the arithmetic mean of a and b.

If a,b,c in G.P. x,y be the A.M.\'s between a,b and b,c respectively then (a/x+c/y)(b/x+b/y)= (A) 2 (B) -4 (C) 4 (D) none of these

If a^x=b ,\ b^y=c\ a n d\ c^z=a , prove that x y z=1

VMC MODULES ENGLISH-SEQUENCE AND SERIES -LEVEL-1

If every even term of a series is a times the term before it and every...
Text Solution
|
If a^x=b^y=c^z and a,b,c are in G.P. show that 1/x,1/y,1/z are in A.P.
Text Solution
|
If a ,b ,c are in G.P. and x ,y are the arithmetic means of a ,ba n db...
Text Solution
|
If ai > 0 for i=1,2,…., n and a1 a2 … a(n=1) , then minimum value o...
Text Solution
|
Suppose a,b, c are in A.P. and a^(2) , b^(2),c^(2) are in G.P. if a lt...
Text Solution
|
One side of a equilateral triangle is 24 cm. The mid-points of its sid...
Text Solution
|
The sum to infinity of the series 1+2(1-(1)/(n))+3(1-(1)/(n))^(2)+ ....
Text Solution
|
Let an be the nth term of a G.P. of positive numbers. Let sum(n=1)^(10...
Text Solution
|
The sum of the series (1 2/3)^(2) + (2 1/3)^(2) + 3^2 + (3 2/3)^(2) ...
Text Solution
|
The roots of equation x^2+2(a-3)x+9=0 lie between -6 and 1 and 2, h1, ...
Text Solution
|
If a,b,c are real numbers such that 3(a^(2)+b^(2)+c^(2)+1)=2(a+b+c+ab...
Text Solution
|
The number a, b and c are between 2 and 18, such that (i) their su...
Text Solution
|
three number a,b,c are in GP such that : (i) a+b+c=70 (ii) 4a,5b,4c a...
Text Solution
|
If tr denotes the r^(th) term of an G.P. and t1 t5 t10 t16 t21 t25 ...
Text Solution
|
The summation of series sum(r=1->99) 1/(sqrt(r+1)+sqrtr) is:
Text Solution
|
If a,b,c are in A.P. then the roots of the equation (a+b-c)x^2 + (b-a...
Text Solution
|
If sum of first n terms of a series is n/(n+1) find 1/(T8)where T8 is ...
Text Solution
|
if (1+3+5+7+....(2p-1))+(1+3+5+...+(2q-1)) =1+3+5+...+(2r -1), then le...
Text Solution
|
If S1 ,S2 and S3 denote the sum of first n1,n2 and n3 terms respec...
Text Solution
|
If a, b, c and d are in G.P. show that (a^2+b^2+c^2)(b^2+c^2+d^2)=(a ...
Text Solution
|