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

Question

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

1 : 2 : 3

1 : 3 : 5

2 : 3 : 4

N o n e o f t h ese

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a, b, c

are in A.P.

b - a, c - b

and

a

in G.P., then

a : b : c

5 mins ago

Discuss this question LIVE

5 mins ago

Text solutionVerified

Given,

a, b, c

are in A.P. then

b - a = c - b

......(1).

Also given

b - a, c - b, a

are in G.P.

Then

(c - b)^{2} = a (b - a)

Using (1) we get,

(c - b) = a

or,

c = a + b

......(2).

Using this in (1) we get,

b - a = a

or,

b = 2 a

Using this value of

b

in (2) we get,

c = 3 a

So,

a : b : c = a : 2 a : 3 a = 1 : 2 : 3

. [ Using vales of

b, c

]

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Question Text	If $a, b, c$ are in A.P. $b - a, c - b$ and $a$ in G.P., then $a : b : c$ is
Answer Type	Text solution:1
Upvotes	150

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

Text solutionVerified

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