Question

if the first and fourth terms of a GP are 9 and 72 respectively find the common ratio also find the sum of first 7 terms? Note:let A be Airthematic mean and G be a geometric mean of a&b then A=a+b/2 and G=√ab.A≥G.​

Answer 1

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.

Step-by-step explanation:

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