Remember that finding terms in a geometric sequence is done by multiplying the previous term by a common ratio
. For example, we can say:


We have
. To find
, let's multiply this term by
:

Now, let's use this to find all of our other terms:



Thus, our terms are 64, 80, 100, 125, and (625/4).
The Pythagorean theorem states that the square of the hypotenuse is equal to the sum of the squares of the legs:

The hypotenuse is the side with the greatest length.
Check all options:
1. c=5, a=3, b=4:
true.
2. c=14, a=4, b=11:
false.
3. c=17, a=9, b=14:
false.
4. c=16, a=8, b=14:
false.
5. c=17, a=8, b=15:
true.
Answer: correct options are A and E.
Again using the Pythagorean Theorem:
h^2=x^2+y^2, where h is the hypotenuse of a right triangle and x and y are the side lengths. You are given that the hypotenuse is 34 ft and the base side is 16ft. Let h=34, x=16, and y=height, then you have:
34^2=16^2+y^2
y^2=34^2-16^2
y^2=1156-256
y^2=900
y=√900
y=30 ft
So the ladder will reach a spot 30 feet high on the building.
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