Questions from Geometry Homework?

Question

Find the next three numbers?

8, -4, 2, -1, 1/2

1, 3, 9, 27

3, 36, 9, 108, 27
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Find the angles of a triangle

The largest angle is 3 times bigger than the smallest angle. The third angle is 2 times bigger than the smallest angle. Find all the angles

Answer 1

1) The sequence is alternating +/- and declining by half in absolute value. In other words, each new value is determined from the previous value by multiplying with -1/2.

 

Next three numbers:  -1/4, 1/8, -1/16

 

2) Similar, this time the factor is 3.

 

Next three numbers: 81, 243, 729

 

3) You have the same sequence as in 2)  (i.e. 3, 9, 27) but this time the sub-sequence in between is 12 times the value of the elements of the first sequence.  I.e. 3·12 = 36, 9·12 = 108.

 

Next three numbers: 324, 81, 972

 

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The wording of the problem is somewhat ambiguous. Strictly speaking, "three times bigger" means "four times as big." I am assuming that by "three times bigger" the author actually means "three times as big as..."

 

The sum of the angles in a triangle is 180 degrees.

Say the largest angle is x, the next angle is y, and the smallest angle is z.

 

x = 3z

y = 2z

x+y+z = 180

 

Plug in the first two equations into the third one, you get:  3z + 2z + z = 180,  or   6z = 180.

 

Therefore, z = 30 (smallest angle).

x = 3z = 90 (largest angle).

y = 2z = 60 (third angle).