Insert 5 geometric means between 16 and $$\dfrac{1}{4}$$.

Asked by Aaryan | 1 year ago |  151

##### Solution :-

Let the five terms be a1, a2, a3, a4, a5.

A = 27, B = $$\dfrac{1}{4}$$

Now, these 5 terms are between A and B.

So the GP is: A, a1, a2, a3, a4, a5, B.

So we now have 7 terms in GP with the first term being 16 and seventh being $$\dfrac{1}{4}$$.

We know that, Tn = arn–1

Here, Tn = $$\dfrac{1}{4}$$, a = 16 and

$$\dfrac{1}{4}$$ = 16r7-1

$$\dfrac{1}{(4×16)}$$ = r6

r = $$\dfrac{1}{2}$$

a1 = Ar == 8

a2 = Ar2 = 4

a3 = Ar3  = 2

a4 = Ar4 = 1

a5 = Ar5 = $$\dfrac{1}{2}$$

The five GM between 16 and $$\dfrac{1}{4}$$ are 8, 4, 2, 1, $$\dfrac{1}{2}$$

Answered by Aaryan | 1 year ago

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