If a,b, and c are in A.P and b-a,c-b an...

If a,b, and c are in A.P and b-a,c-b and a are in G.P then a:b:c is

A

`1:2:3`

B

`1:3:5`

C

`2:3:4`

D

`1:2:4`

Text Solution

Verified by Experts

The correct Answer is:

A

We have
2b=a+c
`(c-b)^(2)=(b-a)a`
`rArr(b-a)^(2)=(b-a)a [2b=a+crArrb-a=c-b]`
`rArrb=2a`
`rArrc=3a`
`rArra:b:c=1:2:3`

Promotional Banner

Promotional Banner

Topper's Solved these Questions

PROGRESSION AND SERIES
CENGAGE PUBLICATION|Exercise EXERCIESE ( MULTIPLE CORRECT ANSWER TYPE )|66 Videos
PROGRESSION AND SERIES
CENGAGE PUBLICATION|Exercise EXERCIESE ( LINKED COMPREHENSION TYPE )|60 Videos
PROGRESSION AND SERIES
CENGAGE PUBLICATION|Exercise CONCEPT APPLICATION EXERICISE 5.9|9 Videos
PROBABILITY II
CENGAGE PUBLICATION|Exercise MULTIPLE CORRECT ANSWER TYPE|6 Videos
PROPERTIES AND SOLUTIONS OF TRIANGLE
CENGAGE PUBLICATION|Exercise Archives (Numerical Value Type)|3 Videos

Similar Questions

Explore conceptually related problems

a ,b ,c x in R^+ such that a ,b ,and c are in A.P. and b ,c and d are in H.P., then a b=c d b. a c=b d c. b c=a d d. none of these

If a,b, and c are in G.P then a+b,2b and b+ c are in

If a , b , c , are three unequal number such that a , b ,c are in A.P and (b-a),(c-b) , a are in G.P then find a: b: c .

If a,b,c are in A.P .then 3^a , 3^b and 3^c are in

If a,b,c are three unequal numbers such that a,b,c are in A.P. and (b-a) ,. (c-b) ,a are in G.P., then the value of a:b: c is-

If a, c, b are in A.P. and b, c, d are in G.P. prove that, b, (b-c), (d-a) are in G.P.

Three unequal numbers a, b, c are in A.P. and a, (b-a), (c-a) are in G.P. Prove that, a : b : c = 1 : 3 : 5 .

a,b and c are in A.P. Prove that b+c , c+a and a+b are in A.P.

If a, b, c, d are in A.P. and a, b, c, d are in G.P., show that a^(2) - d^(2) = 3(b^(2) - ad) .

If a ,b ,c are in G.P. and a-b ,c-a ,a n db-c are in H.P., then prove that a+4b+c is equal to 0.

CENGAGE PUBLICATION-PROGRESSION AND SERIES-EXERCIESE ( SINGLE CORRECT ANSWER TYPE )

Let {tn} be a sequence of integers in G.P. in which t4: t6=1:4 and t2+...
Text Solution
|
if x , 2y and 3z are in AP where the distinct numbers x, yand z ar...
Text Solution
|
If a,b, and c are in A.P and b-a,c-b and a are in G.P then a:b:c is
Text Solution
|
If the sides of a triangle are in G.P., and its largest angle is twice...
Text Solution
|
If x ,y ,z are in G.P. and a^x=b^y=c^z , then (log)b a=(log)a c b. (lo...
Text Solution
|
The number of terms common between the series 1+ 2 + 4 + 8..... to 100...
Text Solution
|
If a^2+b^2,a b+b c ,a n db^2+c^2 are in G.P., then a ,b ,c are in a. A...
Text Solution
|
In a G.P. the first, third, and fifth terms may be considered as the ...
Text Solution
|
If the pth ,qth and rth terms of an AP are in G.P then the common rati...
Text Solution
|
If pth, qth , rth and sth terms of an AP are in GP then show that (p-q...
Text Solution
|
If a ,b , a n dc are in G.P. and x ,y , respectively, are the arithmet...
Text Solution
|
If a ,ba n dc are in A.P., and pa n dp ' are respectively, A.M. and G....
Text Solution
|
If (1+x)(1+x^2)(1+x^4)….(1+x^(128))=Sigma(r=0)^(n) x^r, then n is equa...
Text Solution
|
If (1-p)(1+3x+9x^2+27 x^3+81 x^4+243 x^5)=1-p^6,p!=1 , then the value ...
Text Solution
|
Consider the ten numbers a r ,a r^2, a r^3, ,a r^(10)dot If their sum...
Text Solution
|
If x ,y ,a n dz are distinct prime numbers, then (a).x , y , a n dz ma...
Text Solution
|
If a = underset(55 "times")underbrace(111.....1), b= 1+10+10^(2)+10^(3...
Text Solution
|
Let an be the nth therm of a G.P of positive numbers .Let Sigma(n=1)^(...
Text Solution
|
The sum of 20 terms of a series of which every even term is 2 times ...
Text Solution
|
Let a in (0,1) satisfies the equation a^(2008)-2a+1=0v a l u e s(s)toS...
Text Solution
|