Question

Insert two numbers between 1 and -27 so that the resulting sequence is a G.P-Explain in detail guys​

Answer 1

Answer:

-3,-9(r=-3)(r----->common ratio)

Step-by-step explanation:

r=(b÷a)^(1÷(n+1))

since, a is first term and b is last term

therefore, r=(-27)^(1÷3)=-3

so the required g.p.; a,ar,ar^2,ar^3 is;

1,-3,-9,-27

Answer 2

The G.P form is 1, -3, 9, -27.

Step-by-step explanation:

We know, to insert n numbers between a and b

The common ratio is given by,

$r=(\frac{b}{a})^{\frac{1}{n+1}}$

Now, we insert two numbers between 1 and -27.

Here, a=1 and b=-27

n is the number of terms inserted i.e. n=2

So, $r=(\frac{-27}{1})^{\frac{1}{2+1}}$

$r=(-27)^{\frac{1}{3}}$

$r=(-3^3)^{\frac{1}{3}}$

$r=(-3)^{\frac{3}{3}}$

$r=(-3)^1$

$r=-3$

Now, a=1, r=-3

The inserted terms are

$ar=(1)(-3)=-3$

$ar^2=(1)(-3)^2=9$

The G.P form is 1, -3, 9, -27.

# Learn more

Insert two numbers between 3 and 24 so that the resulting sequence is a G.P.

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