The number q is a quotient of a geometric sequence (with positive terms). For which
of the following numbers q can three consecutive terms of the geometric sequence
be lengths of sides of a triangle?
Answers
Given : The number q is a quotient of a geometric sequence (with positive terms)
To Find : For which of the following numbers q can three consecutive terms of the geometric sequence be lengths of sides of a triangle
A q= 0.25
B q=0.5
С q= 1.5
D) q= 2
Solution:
Sum of any two sides of a triangle is greater than third side.
Let say one side is 16x
A q= 0.25
second side = 16x * 0.25 = 4x
third side = 4x * 0.25 = x
x + 4x < 16x Hence it can not form a triangle
A q= 0.5
second side = 16x * 0. 5 = 8x
third side = 8x * 0. 5 = 4x
8x + 4x < 16x Hence it can not form a triangle
q= 1.5
second side = 16x * 1. 5 = 24x
third side = 24x * 1. 5 = 36x
16 x + 24x > 36 x
24x + 36x > 16x
16x + 36x > 24x
Hence it can form a triangle
q= 2
16x , 32x and 64x
16x + 32x < 64x can not form a triangle
For q= 1.5 three consecutive terms of the geometric sequence
be lengths of sides of a triangle
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