Question

If a, b, c are first three terms of a G.P. and the harmonic mean of a and bis 20 and arithmetic mean of
b&c is 5, then
(A) no term of this G.P. is square of an integer
(B) arithmetic mean of a, b, c is 5
(C) b= 16
(D) common ratio of this G.P. is 2

Answer 1

MARK AS BRAINLIEST PLEASE.

Step-by-step explanation:

ANSWER

a,b,c are first three terms of a G.P. The harmonic mean of a and b is 20 and arithmetic mean of b & c is 5

i.e

a+b

2ab

=20 and

2

b+c

=5

let r be the common ratio of given G.P.

∴b=ar,c=ar

2

from (1)

a+ar

2a

2

r

=20 ⇒

1+r

ar

=10 ---(2)

2

ar+ar

2

=5 ⇒ar(1+r)=10 ----(3)

from (2) and (3)

ar=10 and 1+r=1 not possible

or ar=−10 and 1+r=−1

∴a=5 and r=−2

⇒ first three terms of given G.P are 5,−10,20

∴ no term of this G.P. is square of an integer.

3

a+b+c

=

3

5−10+20

=5

∴ Arithmetic mean of a,b,c is 5

Hence, options A and B.