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Nth Term of a GP

If three succ...

Question

If three successive terms of a G.P with common ratio r (r > 1) form the sides of a triangle ABC and [r] denotes greatest integer function, then modulus of [-r] + [r] is

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Solution

Let us suppose the sides of the triangle be a, ar and ar² (being the largest side as r > 1).

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Similar questions

Q. If the sides

a, b, c

A B C

form successive terms of G.P. with common ratio

r (> 1)

then which of the following is correct?

Q. The three successive terms of a GP will form the sides of a triangle if the common ratio

r

(r > 1)

Q. If the sides

a, b, c

A B C

form successive terms of G.P. with common ratio

r (> 1)

then which of the following is correct?

The sum of three terms of a strictly increasing G.P is

α S

and the sum of the squares of these terms is

S^{2}

α^{2} = 2

, then the value of

[r]

[.]

denotes the Greatest Integer function and

r

is the common ratio of the Geometric progression.)

a_{1}

a_{2}

a_{3}

a_{1} > 0)

are three successive terms of a G.P. with common ratio r, then find the value of r for which

a_{3} > 4 a_{2} - 3 a_{1}

.

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