# Let a1,a2,a3,a4,a5  be a G.P. of positive real numbers such that the A.M. of  a2 and a4 is 117 and the G.M. of  a2 and a4 is 108.Then the A.M. of a1 and a5 is : Option 1) 145.5 Option 2) 108 Option 3) 117 Option 4) 144.5

As we learnt in

Common ratio of a GP (r) -

The ratio of two consecutive terms of a GP

- wherein

eg: in 2, 4, 8, 16, - - - - - - -

r = 2

and in 100, 10, 1, 1/10 - - - - - - -

r = 1/10

Let G1=G

so that G2=Gr

G3=Gr2

G4=Gr3

G5=Gr4

If G1, G2, G3, G4, G5, in G.P.

G2+G4=234

G2G4=(108)2

Then

So that

(i)

and

(ii)

from (i) and (ii)

Option 1)

145.5

This option is correct

Option 2)

108

This option is incorrect

Option 3)

117

This option is incorrect

Option 4)

144.5

This option is incorrect

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