Q. 35.0( 1 Vote )

# Insert 5 geometric means between and .

Answer :

Let the five terms be a_{1}, a_{2}, a_{3}, a_{4}, a_{5}.

And,

Now these 5 terms are between A and B.

∴ A, a_{1}, a_{2}, a_{3}, a_{4}, a_{5}, B.

Now all of them are in GP

So we now have 7 terms in GP with the first term being 32/9 and seventh being 81/2.

∴ T_{n} = ar^{n}^{–1}

Here T_{n} = , a = and

⇒

⇒

⇒

∴ a_{1} = Ar =

a_{2} = Ar^{2} =

a_{3} = Ar^{3} =

a_{4} = Ar^{4} =

a_{5} = Ar^{5} =

∴ The six GM between 16 and 1/4 are .

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